one hot assignment

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9.6 ONE-HOT ENCODING METHOD

One-hot encoding is an alternative state assignment method which attempts to minimize the combinational logic by increasing the number of flip-flops. The goal of the method is to try to reduce the number of connections between the logic gates in the combinational circuit of the FSM. The presence of more gate interconnections results into longer propagation delays and a slower FSM. Since the propagation delay through the flip-flops is faster, FSMs require fewer logic gates but not necessarily fewer flip-flops.

Figure 9.26 Logic Implementation of the FSM in Figure 9.24

One-hot encoding assigns one flip-flop for each state. For example, a finite-state machine with N states requires N flip-flops. The states are assigned N -bit binary numbers; where only the corresponding bit position is equal to 1, the remaining bits are equal to0. For example, in a finite-state machine with four states S 0 , S 1 , S 2 , and S 3 , the states are assigned the binary values 0001, 0010, 0100, and 1000, respectively. Notice that only one bit position is equal to 1; the other bits are all equal to 0. The reamaining 12 binary combinations are assigned to don't-care states. Consider the Mealy-type finite-state machine described by the state diagram shown in Figure 9.19 . The state diagram has three states: S 0 , S 1 , and S 2 . One-hot encoding assigns the binary number values 001, 010, and 100 ...

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Comparing Binary, Gray, and One-Hot Encoding

Join our engineering community sign-in with:, this article shows a comparison of the implementations that result from using binary, gray, and one-hot encodings to implement state machines in an fpga. these encodings are often evaluated and applied by the synthesis and implementation tools, so it’s important to know why the software makes these decisions..

Finite state machines (FSMs) are a very common part of nearly every digital system. That’s why synthesis tools often inspect your code to detect FSMs and perform optimizations that may modify the encoding of the states. It doesn’t matter if you carefully selected and specified the values that implement your states in your source code, the synthesis tool may replace those values with others that may even have a different bit length than your original encoding.

If you’d like to brush up on implementing state machines in Verilog, you should read my article titled Creating Finite State Machines in Verilog .

Encoding of States: Gray vs. Binary vs. One-Hot

The three most popular encodings for FSM states are binary, Gray, and one-hot.

Binary Encoding

Binary encoding is the straightforward method you may intuitively use when you assign values sequentially to your states. This way, you are using as few bits as possible to encode your states.

An example of one-hot encoding. Image by Steve Arar

Gray encoding.

Gray code consists of a sequence where only one bit changes between one value and the next. In addition to also using the minimum number of bits, this encoding minimizes dynamic power consumption if the sequence of states is followed optimally.

The Gray code wheel. Image from Marie Christiano

One-hot encoding.

Finally, one-hot encoding consists in using one bit representing each state, so that at any point in time, a state will be encoded as a 1 in the bit that represents the current state, and 0 in all other bits. This may not seem very efficient at first because of the number of bits used, and the excessive number of invalid states. However, one-hot encoding is very good at simplifying the stimulus logic for the flip flops because there’s no need to decode the states. The bits are  the states. 

For more on state encodings, you may want to check out the article Encoding the States of a Finite State Machine in VHDL  by Steve Arar.

Which Encoding Is the Best?

This is a tough question, mostly because each encoding has its benefits and shortcomings, so it comes down to an optimization problem that depends on a large number of factors.

• If a very simple system yields very similar results across encodings, then the original encoding is the best choice.
• If the FSM cycles through its states in one path (like a counter) then Gray code is a very good choice.
• If the FSM has an arbitrary set of state transitions or is expected to run at high frequencies, maybe one-hot encoding is the way to go.

Now, all of these claims are just educated guesses, and finding the optimal state assignment is a complicated problem. Because of this, my official advice is to let the compiler decide for you. That said, I decided to run a comparison of the results for these three encodings in three different development tools and three different state machines.

In the next article, we'll discuss the results of my experiments.

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Best Practices for One-Hot State Machine, coding in Verilog

There are 3 main points to making high speed state machines by one-hot encoding:

• Use 'parallel_case' and 'full_case' directives on a 'case (1'b1)' statement
• Use state[3] style to represent the current state
• Assign next state by:
• default assignment of 0 to state vector
• fully specify all conditions of next state assignments, including staying in current state.

Also, these points are also recommended:

• Separate the code for next state assignment from output logic/assignments.
• Use parameters to assign state encoding (or `define)
• use continuous assignments,
• set/reset at specific conditions, holding value at all other times

(the designer should choose based on complexity of generated logic)

Simple example:

reg [2:0]  state ; parameter  IDLE=0, RUN=1, DONE=2 ; always @ (posedge clock or negedge resetl)   if ( ! resetl) begin     state <= 3'b001 ;     out1 <= 0 ;   end   else begin state <= 3'b000 ; case (1'b1) // synthesis parallel_case full_case   state[IDLE]: if (go)   state[RUN] <= 1 ; else   state[IDLE] <= 1 ;

  state[RUN]:

if (finished)   state[DONE] <= 1 ; else   state[RUN] <= 1 ;

  state[DONE]:

state[IDLE] <= 1 ;

out1 <= state[RUN] & ! finished ;

If you want to read more in depth about all of these points, including why one-hot is useful for high speed, read this longer writeup .

I arrived at the conclusions here on my own, but around the same time, Cliff Cummings presented a paper at SNUG San Jose 2003 that included these same points: Cliff's paper Cliff's website

Verilog Pro

One-hot State Machine in SystemVerilog – Reverse Case Statement

Finite state machine (FSM) is one of the first topics taught in any digital design course, yet coding one is not as easy as first meets the eye. There are Moore and Mealy state machines, encoded and one-hot state encoding, one or two or three always block coding styles. Recently I was reviewing a coworker’s RTL code and came across a SystemVerilog one-hot state machine coding style that I was not familiar with. Needless to say, it became a mini research topic resulting in this blog post.

When coding state machines in Verilog or SystemVerilog, there are a few general guidelines that can apply to any state machine:

• If coding in Verilog, use parameters to define state encodings instead of ‘define macro definition. Verilog ‘define macros have global scope; a macro defined in one module can easily be redefined by a macro with the same name in a different module compiled later, leading to macro redefinition warnings and unexpected bugs.
• If coding in SystemVerilog, use enumerated types to define state encodings.
• Always define a parameter or enumerated type value for each state so you don’t leave it to the synthesis tool to choose a value for you. Otherwise it can make for a very difficult ECO when it comes time to reverse engineer the gate level netlist.
• Make curr_state and next_state declarations right after the parameter or enumerated type assignments. This is simply clean coding style.
• Code all sequential always block using nonblocking assignments (<=). This helps guard against simulation race conditions.
• Code all combinational always block using blocking assignments (=). This helps guard against simulation race conditions.

SystemVerilog enumerated types are especially useful for coding state machines. An example of using an enumerated type as the state variable is shown below.

Notice that enumerated types allow X assignments. Enumerated types can be displayed as names in simulator waveforms, which eliminates the need of a Verilog trick to display the state name in waveform as a variable in ASCII encoding.

One-hot refers to how each of the states is encoded in the state vector. In a one-hot state machine, the state vector has as many bits as number of states. Each bit represents a single state, and only one bit can be set at a time— one-hot . A one-hot state machine is generally faster than a state machine with encoded states because of the lack of state decoding logic.

SystemVerilog and Verilog has a unique (pun intended) and efficient coding style for coding one-hot state machines. This coding style uses what is called a reverse case statement to test if a case item is true by using a case header of the form case (1’b1) . Example code is shown below:

In this one-hot state machine coding style, the state parameters or enumerated type values represent indices into the state and next vectors. Synthesis tools interpret this coding style efficiently and generates output assignment and next state logic that does only 1-bit comparison against the state vectors. Notice also the use of always_comb and always_ff SystemVerilog always statements, and unique case to add some run-time checking.

An alternate one-hot state machine coding style to the “index-parameter” style is to completely specify the one-hot encoding for the state vectors, as shown below:

According to Cliff Cummings’ 2003 paper , this coding style yields poor performance because the Design Compiler infers a full 4-bit comparison against the state vector, in effect defeating the speed advantage of a one-hot state machine. However, the experiments conducted in this paper were done in 2003, and I suspect synthesis tools have become smarter since then.

State machines may look easy on paper, but are often not so easy in practice. Given how frequently state machines appear in designs, it is important for every RTL designer to develop a consistent and efficient style for coding them. One-hot state machines are generally preferred in applications that can trade-off area for a speed advantage. This article demonstrated how they can be coded in Verilog and SystemVerilog using a unique and very efficient “reverse case statement” coding style. It is a technique that should be in every RTL designer’s arsenal.

What are your experiences with coding one-hot state machines? Do you have another coding style or synthesis results to share? Leave a comment below!

• Synthesizable Finite State Machine Design Techniques Using the New SystemVerilog 3.0 Enhancements

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14 thoughts on “One-hot State Machine in SystemVerilog – Reverse Case Statement”

I am enjoying reading your blog, but I believe you are missing something from your one-hot reverse-case example above. In Cliff’s paper, the enumerated type is used as an index to a vector – you neglected to copy this part over. I believe the correct code would look like this:

enum { IDLE = 0, READ = 1, DLY = 2, DONE = 3 } state_index_t;

logic [3:0] state, next;

with the vector declaration in place the rest of the example above should work OK.

Hi John, thanks for your comment! You’re correct that in Cliff’s paper the enumerated type is used as an index into the one-hot vector. In my original code above I was sloppy and mixed the value of the enumerated type (0, 1, 2, 3) with the type itself. While I did test the original code and it simulated correctly, I’m sure a linting tool would give a warning about the improper usage. I have made a correction to the code above.

Great post. I have seen improved performance with one hot reverse case statements as well. One comment I would have is that the default assignment for “next” should be a valid case especially since we don’t have a default case statement. In the case of a bit being flipped because of some rare condition you’ll be able to recover. Something like this:

// Combinational next state logic always_comb begin next = ‘0; next[IDLE] = 1’b1; // ADDED unique case (1’b1) state[IDLE] : begin if (go) begin next = ‘0; // ADDED next[READ] = 1’b1; end else begin next = ‘0; // ADDED next[IDLE] = 1’b1; end end

Thanks, Amol, for your suggestion. I understand your reasoning to have a valid case (like IDLE) be the default transition for safety. Personally I don’t code that way as I think a bit flip anywhere in the chip is considered fatal, and even if the affected state machine returns to IDLE, it will likely have become out of sync with other logic and state machines. However, I have coworkers who code in the way you suggested as well.

There is a subtle point that may cause your code to not behave in the way intended. Due to the use of “unique case” in the code, I think for any unspecified cases (e.g. if a bit flip causes the state vector to become 4’b0000; 4’b0000 is not a case that is listed in the case statement), the synthesis tool is free to infer any logic (specifically to the “next” vector), so there’s no guarantee the default “next[IDLE]=1’b1” wouldn’t be overridden by other logic the synthesis tool inferred. See my post on SystemVerilog unique keyword.

Interesting. I had a “typo” in my code recently that caused the case_expression to be one not listed in the case statement and I did observe odd behavior from what I would have expected. So I guess having the default “next[IDLE]=1’b1” is probably not that useful here. 🙂

This is a synthetic example I would assume but want to get your feedback on preserving X-propagation. Bugs in the state machine next state logic or outside the state machine driving the input signals “go” and “ws” can be hidden by the current way of coding (using if-else and also default assigned to 0). Killing x-prop can cause “simulation vs. synthesis mismatch”, which can be pretty fatal. Consider this improvement:

// Combinational next state logic always_comb begin //next = ‘0; // Comment out; see added default in case statement instead unique case (1’b1) state[IDLE] : begin // Ensures x-prop if go === x next[READ] = go == 1’b1; next[IDLE] = go == 1’b0; end state[READ] : next[ DLY] = 1’b1; state[ DLY] : begin // Ensures x-prop if ws === x next[DONE] = ws == 1’b0; next[READ] = ws == 1’b1; end state[DONE] : next[IDLE] = 1’b1; // Add default to propagate Xs for unhandled states or if state reg went X itself default: next <= 'x; endcase end

Hi VK, thanks for your comment! When you say the code “kills x-prop”, I think you mean that if “ws” or “go” input has the value of X, then the “if(x)-else” coding style will take on the “else” case, rather than also corrupting the outputs (in this case the “next” vector)? Yes you’re right, and I’ll admit I’ve coded this kind of bug before! Recently our team has turned on the Synopsys VCS x-propagation feature to detect this kind of problem. It corrupts the output even with this “if-else” coding style (see my post on x-prop ). If that’s not available, then yes, the code you propose will also do the job. Previously I also coded a “default: next <= 'x" in my state machines, but the RTL linting tool we use complains about this, so I've moved away from this style. VCS x-prop will also catch this kind of problem.

I just realized you are not driving every bit of “next” in the case statement, so you would need to have the default next = ‘0 at the beginning as you did originally. That would not kill x-prop anyways since the default in the case statement would override it if needed.

Hello Jason, Thanks for the post. It really helped me to understand more about OneHot FSMs. The statement on Cliff’s paper in 2003 is not entirely true. we can handle that case by adding a unique key word. In the meantime concern raised by VK is great and worth looking into. with both of this I would like you to consider the following code which will give you the same synthesis result. Advantages being 1) state vector is enum, hence waveform visualization is better 2) does propagate x, in case FSM assignment is buggy 3) simpler and easy to read

typedef enum logic [3:0] { IDLE = 4’b0001, READ = 4’b0010, DLY = 4’b0100, DONE = 4’b1000, SX = 4’x } state_t; state_t state, next;

// Sequential state transition always_ff @(posedge clk or negedge rst_n) if (!rst_n) state <= IDLE; else state <= next;

// Combinational next state logic always_comb begin next = SX; unique case (state) IDLE : begin if (go) next = READ; else next = IDLE; end READ : next = DLY; DLY : begin if (!ws) next = DONE; else next = READ; end DONE : next = IDLE; endcase end

// Make output assignments always_ff @(posedge clk or negedge rst_n) …

Thanks for your comments! Yes I had been intending to make an update to this page for while, especially about your first point on waveform display of the state vector. After simulating my coworker’s code in the original coding style, I also realized simulators do not visualize state vectors written this way very well. I would agree that specifying the one-hot state encoding in the enum type should be equivalent and will display better. Your proposed code is indeed how I would write a one-hot state machine using SystemVerilog today!

Hi Jason Reffering to the last comment by shailesh, do you still suggests using “reverse case method” for FSM ? is it worth the less-readable code? or that shailesh’s code will do the same w/o infers the full bit comparison? this code is much more initiuative, but what about performence?

I have not had a chance to look closely at the synthesized netlist of a one-hot encoded state machine written with enumerated type and regular case statement. I believe with today’s compiler technology it should synthesize the same as the reverse case statement method (i.e. optimized to do single state bit comparisons). I coded my most recent design this way based on this belief. I’ll let you know when I can verify exactly the gates that Design Compiler synthesized 🙂

Thanks for the article, Jason. Your articles have helped answer many questions I’ve had. My colleague and I were discussing about this recently and a question came up – Are reverse case statements useful at all in plain Verilog (not System Verilog) if one isn’t allowed to use synthesis pragmas such as ‘parallel_case’? Unlike System Verilog, Verilog doesn’t have the ‘unique’ keyword.

Put in another way, the question is what really happens when one codes a reverse case statement in Verilog with no ‘parallel_case’ directive. Does synthesis assume that the input to the case-statement is not parallel and hence not one-hot and hence infer priority logic? I’d love to hear your thoughts.

I think if coded correctly, the reverse case statement FSM coding style should automatically create a case statement that is parallel, without requiring the ‘parallel_case’ directive. Since each state is represented by a unique number, each case expression is effectively comparing 1 unique register bit against 1’b1. Therefore no overlap between the different case expressions should be possible, which matches the definition of parallel case.

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Finite State Machine (FSM) encoding in VHDL: binary, one-hot, and others

State diagram in Sigasi Visual HDL Professional

In VHDL, Finite State Machines (FSMs) can be written in various ways. This article addresses the encoding of, and the data types used, for the state register . The encoding of the states of an FSM affects its performance in terms of speed, resource usage (registers, logic) and potentially power consumption. As we will see, enumerated datatypes are preferred for clarity and easy of maintenance .

State encoding algorithms include:

• Binary encoding : states are enumerated with binary encoded numbers: "000" , "001" , "010" , "011" , "100" …
• One-hot encoding : states are represented as bit patterns with exactly 1 '1' : "000001" , "000010" , "000100" , "001000" , "010000" …
• Gray coding : the encoding of successive states only differ by one bit: "000" , "001" , "011" , "010" , "110" …

The preferred encoding depends on the nature of the design. Binary encoding minimizes the length of the state vector, which is good for CPLD designs. One-hot encoding is usually faster and uses more registers and less logic. That makes one-hot encoding more suitable for FPGA designs where registers are usually abundant. Gray encoding will reduce glitches in an FSM with limited or no branches.

FSMs should be designed such that they’re easy to understand and maintain . At the same time, the designer must retain control of the FSM’s state encoding . Generally speaking, a state register can be implemented in two different ways: either as a vector type or as an enumeration type .

Consider the following examples:

With a vector type , the designer has perfect control over the encoding of the state vector. However, it is hard to know what each state means and changes are cumbersome . If a state needs to be inserted, the encoding of all further states need to be updated wherever used.

With an enumeration type , the design becomes much easier to understand and maintain :

States can be added or modified easily, and other states are not affected when one state is added or modified. The encoding of the states however is magically implemented by the RTL synthesis tool. Fortunately, most RTL synthesis tools have ways for the designer to control the state encoding of enumerated state types.

In many cases, one would like to define the state encoding style . The example below shows how that can be achieved at the type level :

The enum_encoding defines the FSM’s state encoding style. Support of enumeration encoding styles differs between RTL synthesis tools , so have a look at the manual of yours for supported styles. Also, some RTL synthesis tools e.g. Xilinx XST and Synopsys Synplify require additional settings for the enum_encoding attribute to take effect.

Alternatively, the state encoding style can be defined at the signal level rather than at the type level. The fsm_state is used for that purpose. This way, multiple FSMs with the same set of states can each have a different state encoding. The allowed values are: BINARY , GRAY , ONE_HOT , ONE_COLD or AUTO . With Synopsys Synplify, use attribute syn_encoding instead of fsm_state .

In the above examples, only the encoding style of the state vector is defined. Using the enum_encoding attribute, the designer can also fully control the encoding of each individual state . If a state is added, its encoding needs to be added in the attribute. The example below shows how that can be achieved.

In conclusion, enumerated types are preferred for FSM state vectors . Well chosen enumeration literals make the FSM more easy to read, understand and maintain . With an enumerated type, states can be added to or removed from the FSM without affecting the other states. The size of the state vector will be adjusted during RTL synthesis. Still, the designer retains as much control of the state encoding as they desire.

• Records in VHDL: Initialization and Constraining unconstrained fields (blog post)
• Using Sigasi Studio's Graphics Configuration (legacy)
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• Signal Assignments in VHDL: with/select, when/else and case (blog post)
• VHDL Pragmas (blog post)

Bayes Classifier VS Regression Function #

Consider the two-class classification problem with a label set given by $\mathcal{Y}=\{-1,1\}$, without loss of generality. The regression function for the binary variable $Y$ is given by $$\begin{align*} \mu(x)=&\mathbb{E}[Y\mid X=x]\\=&\mathbb{P}(Y=1\mid X=x)\cdot 1\\&+\mathbb{P}(Y=-1\mid X=x)\cdot (-1)\\=&\mathbb{P}(Y=1\mid X=x)\\&-\mathbb{P}(Y=-1\mid X=x).\end{align*} $$

The Bayes classifier becomes nothing else but the sign of the regression function

$$ \underset{y\in\{-1,1\}}{\operatorname{argmax}}~\mathbb{P}(Y=y\mid X=x) =\operatorname{sign}(\mu(x)) $$

except for the feature values at the decision boundary $\{x:\mu(x)=0\}$ for which we can arbitrarily assign the labels.

Multiple-Class Classification #

What if we have multiple labels, say, with $\mathcal{Y}=\{\mathcal{C}_1,\ldots,\mathcal{C}_K\}$ for some finite $K\geq 2$? Unfortunately, the sign trick above is insufficient to distinguish more than two classes. To handle more classes, we need to encode the categorical target using a vector of dummy variables.

One-Hot Encoding # The one-hot encoding of categorical target $Y\in \{\mathcal{C}_1,\ldots,\mathcal{C}_K\}$ is the vector given by $$(Y^{(1)},\ldots,Y^{(K)})\in \{0,1\}^K$$ with $$Y^{(k)}=\mathbf{1}[Y=\mathcal{C}_k],~1\leq k\leq K$$ where $\mathbf{1}[A]$ denotes the indicator function that equals to 1 if condition $A$ is satisfied and equals to 0 otherwise.

In this example, there are $K=3$ teams with labels A, B, and C. We convert each observation of the label A/B/C into a vector of 3 dummies.

The $K$-dimensional regression function for the one-hot encoded target is given by

$$\mu(x)=(\mu_1(x),\ldots,\mu_K(x))$$ where $$\begin{align*}\mu_k(x)=&\mathbb{E}[Y^{(k)}\mid X=x]\\=&\mathbb{P}\left( Y=\mathcal{C}_k\mid X=x\right).\end{align*}$$

With one-hot encoding, one can now estimate the Bayes classifier using a two-step procedure:

• First estimate the multivariate regression function $\mu(x)$
• Then choose the label $h(x)\in\{\mathcal{C}_1,\ldots,\mathcal{C}_K\}$ with largest regression value.

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vhdl code: one hot encoding of state

if I am using one hot encoding for the states and want to go from S0 -> S1 -> S2 -> S3 -> S0

Apparently the following code does this. However I am not sure how the state assignment part works in the snippet (comments mention rotation of 1 bit...?)... can someone please explain HOW this rotation works ie. why the "&state(2)" etc. It would also be extremely helpful if you could provide a simple hardware representation of the code snippet.

In the architecture we are told that S0 = 0001, S1 = 0010, S2 = 0100, S3 = 1000

• 1 \$\begingroup\$ There is no reason to be "clever" in your code writing. Write plainly and simply and let the tool optimize. Only when you are fighting for space should you start trying to code tricky like this. There is no value in state <= state(1 downto 0) & state(2) when a clearer and more easily understood case statement would get the same job done. \$\endgroup\$ –  akohlsmith Commented May 22, 2012 at 19:54

2 Answers 2

In practice, you will never explicitly use one hot encoding. Rather, you should design your VHDL file so that you use enumerations instead of explicit states. This allows the synthesis tools that you use to generate your design to come up with their own preferred encoding. In a CPLD, this would probably be dense coding, because gates are more abundant than flip flops. In an FPGA, this would probably be one hot, because flip flops are more abundant. In other random cases, the synther might think that gray coding, or sequential coding, might be better.

However, to answer your question, how does this perform a rotation? (note I am using your original 3-bit state, even though your question regards 4 bit states)

Consider state = "001". Thus, state(1 downto 0) = "01". Also, state(2) = '0'.

Thus, when you do state <= state(1 downto 0) & state(2), you are doing state <= "01" & '0'. This now means state = "010"; a left rotation by one bit.

In plain language, to rotate an n-bit vector to the left by one bit, take the lower n-1 bits, and concatenate the MSB on the right side of it. In this example, it's taking the state(1 downto 0) bits, and concatenating state(2) on the right side.

In contrast, a right rotation would be represented as state <= state(0) & state(2 downto 1). This takes the LSB, and then concatenates the upper n-1 bits on the right side of it. For state = "001", this right rotation would be like state <= '1' & "00". This now means state = "100".

I think the logic is wrong... you've got a four bit state vector, but you are only using three of the bits in any logic. It is obvious that to cycle through the states all you have to do is shift the bits left by one with rotation right? Just make a table showing the state sequence desired:

The hardware for this is just to wire the output of the 4-bit register back on itself with the lines crossed to get the affect above.

Namely: State(0) <= State(3), State(1) <= State(0), State(2) <= State(1), State(3) <= State(2)

The abbreviated way of stating that is to form a new vector from the old one like this:

Not sure my syntax is perfect, but that's the gist of it I believe; I think what I wrote is something like a Verilog/VHDL mashup. Anyway, you just want to express running the wires back to the right place so the 1 shifts left and around each clock.

As @mng noted - the '&' operator concatenates bit vectors together, and does not perform a logical-and, as one might think.

• \$\begingroup\$ how exactly is "--rotate state 1 bit to left" part doing the shifting? In terms of the vhdl syntax? \$\endgroup\$ –  rrazd Commented May 22, 2012 at 3:51
• 5 \$\begingroup\$ In VHDL, the '&' stands for concatenation. \$\endgroup\$ –  mng Commented May 22, 2012 at 4:58
• 1 \$\begingroup\$ @mng I like Verilog's syntax for this better... seems abusive to use & as an operator that doesn't correspond in some way to the 'and' logic operation; anyway yes the VHDL syntax is the key to what the OP was asking (the code is still wrong though) \$\endgroup\$ –  vicatcu Commented May 22, 2012 at 16:10
• \$\begingroup\$ @vicatcu: Seems abusive, because you're used to C. However the BASIC-like language are all consistent in use of AND for the bitwise operator and & for concatenation of strings. \$\endgroup\$ –  Ben Voigt Commented May 22, 2012 at 20:44
• \$\begingroup\$ And ultimately, VHDL's syntax is far cleaner: state <= state ROL 1; . Unfortunately the code in the question didn't use that. \$\endgroup\$ –  Ben Voigt Commented May 22, 2012 at 20:46

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One-Hot Encoding in Scikit-Learn with OneHotEncoder

• February 23, 2022 April 14, 2024

In this tutorial, you’ll learn how to use the OneHotEncoder class in Scikit-Learn to one hot encode your categorical data in sklearn . One-hot encoding is a process by which categorical data (such as nominal data) are converted into numerical features of a dataset. This is often a required preprocessing step since machine learning models require numerical data.

By the end of this tutorial, you’ll have learned:

• What one-hot encoding is and why it’s important in machine learning
• How to use sklearn’s OneHotEncoder class to one-hot encode categorical data
• How to one-hot encode multiple columns
• How to use the ColumnTransformer class to manage multiple transformations

Are you looking to one-hot encode data in Pandas? You can also use the pd.get_dummies() function for this!

Table of Contents

What is One-Hot Encoding?

One-hot encoding is the process by which categorical data are converted into numerical data for use in machine learning. Categorical features are turned into binary features that are “one-hot” encoded, meaning that if a feature is represented by that column, it receives a 1 . Otherwise, it receives a 0 .

This is perhaps better explained by an image:

You may be wondering why we didn’t simply turn the values in the column to, say, {'Biscoe': 1, 'Torgensen': 2, 'Dream': 3} . This would presume a larger difference between Biscoe and Dream than between Biscoe and Torgensen.

While this difference may exist, it isn’t specified in the data and shouldn’t be imagined.

However, if your data is ordinal , meaning that the order matters, then this approach may be appropriate. For example, when comparing shirt sizes, the difference between a Small and a Large is , in fact, bigger than between a Medium and a Large.

Why is One-Hot Encoding Important to Machine Learning?

Now that you understand the basic mechanics of one-hot encoding, you may be wondering how this all relates to machine learning. Because machine learning algorithms assume (and require) your data to be numeric, categorical data must be pre-processed in order for it to be accepted .

Following the example of the Island above – if we were to ask any classification or regression model to be built using the categorical data, an error would be raised. This is because machine learning algorithms cannot work with non-numerical data.

How to Use Sklearn’s OneHotEncoder

Sklearn comes with a one-hot encoding tool built-in: the OneHotEncoder class. The OneHotEncoder class takes an array of data and can be used to one-hot encode the data.

Let’s take a look at the different parameters the class takes:

Let’s see how we can create a one-hot encoded array using a categorical data column. For this, we’ll use the penguins dataset provided in the Seaborn library . We can load this using the load_dataset() function:

Let’s break down what we did here:

• We loaded the dataset into a Pandas DataFrame, df
• We initialized a OneHotEncoder object and assigned it to ohe
• We fitted and transformed our data using the .fit_transform() method
• We returned the array version of the transformed data using the .toarray() method

We can see that each of the resulting three columns are binary values. There are three columns in the array, because there are three unique values in the Island column. The columns are returned alphabetically.

We can access the column labels using the .categories_ attribute of the encoder:

If we wanted to build these columns back into the DataFrame, we could add them as separate columns:

In the next section, you’ll learn how to use the ColumnTransformer class to streamline the way in which you can one-hot encode data.

How to Use ColumnTransformer with OneHotEncoder

The process outlined above demonstrates how to one-hot encode a single column. It’s not the most intuitive approach, however. Sklearn comes with a helper function, make_column_transformer() which aids in the transformations of columns. The function generates ColumnTransformer objects for you and handles the transformations.

This allows us to simply pass in a list of transformations we want to do and the columns to which we want to apply them. It also handles the process of adding the data back into the original dataset. Let’s see how this works:

Let’s see what we did here:

• We imported the make_column_transformer() function
• The function took a tuple containing the transformer we want to apply and the column to which to apply to. In this case, we wanted to use the OneHotEncoder() transformer and apply it to the 'island' column.
• We used the remainder='passthrough' parameter to specify that all other columns should be left untouched.
• We then applied the .fit_transform() method to our DataFrame.
• Finally, we reconstructed the DataFrame

In the next section, you’ll learn how to use the make_column_transformer() function to one-hot encode multiple columns with sklearn.

How to One-Hot Encode Multiple Columns with Scikit-Learn

The make_column_transformer() function makes it easy to one-hot encode multiple columns. In the argument where we specify which columns we want to apply transformations to, we can simply provide a list of additional columns.

Let’s reduce our DataFrame a bit to see what this result will look like:

In this tutorial, you learned how to one-hot encode data using Scikit-Learn’s OneHotEncoder class. You learned what one-hot encoding is and why it matters in machine learning. You then learned how to use the OneHotEncoder class in sklearn to one-hot encode data. Finally, you learned how to use the make_column_transformer helper function for the ColumnTransformer class to one-hot encode multiple columns.

Additional Resources

To learn more about related topics, check out the tutorials below:

• Introduction to Scikit-Learn (sklearn) in Python
• Pandas get dummies (One-Hot Encoding) Explained
• K-Nearest Neighbor (KNN) Algorithm in Python
• Introduction to Random Forests in Scikit-Learn (sklearn)
• Official Documentation: OneHotEncoder

Nik Piepenbreier

Nik is the author of datagy.io and has over a decade of experience working with data analytics, data science, and Python. He specializes in teaching developers how to use Python for data science using hands-on tutorials. View Author posts

4 thoughts on “One-Hot Encoding in Scikit-Learn with OneHotEncoder”

This was very helpful. Thanks!

Thanks so much, Lealdo!

When I used all the imports from the code listings I still got unresolved functions:

AttributeError: ‘ColumnTransformer’ object has no attribute ‘get_feature_names’

Is this just because older versions of ColumTransformer had this function or is there some import not listed?

Sorry for the late reply, Louis! I have fixed the code to what is shown below. Thanks for catching this!

columns=transformer.get_feature_names_out()

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One-Hot Encoding in NLP

Natural Language Processing (NLP) is a quickly expanding discipline that works with computer-human language exchanges. One of the most basic jobs in NLP is to represent text data numerically so that machine learning algorithms can comprehend it. One common method for accomplishing this is one-hot encoding, which converts category variables to binary vectors. In this essay, we’ll look at what one-hot encoding is, why it’s used in NLP, and how to do it in Python .

One of the most basic jobs in natural language processing (NLP) is to describe written data numerically so that machine learning systems can comprehend it. One common method for accomplishing this is one-hot encoding, which converts category variables to binary vectors.

One-Hot Encoding:

One-hot encoding is the process of turning categorical factors into a numerical structure that machine learning algorithms can readily process. It functions by representing each category in a feature as a binary vector of 1s and 0s, with the vector’s size equivalent to the number of potential categories. 

Why One-Hot Encoding is Used in NLP:

• One-hot encoding is used in NLP to encode categorical factors as binary vectors, such as words or part-of-speech identifiers. 
• This approach is helpful because machine learning algorithms generally act on numerical data, so representing text data as numerical vectors are required for these algorithms to work.
• In a sentiment analysis assignment, for example, we might describe each word in a sentence as a one-hot encoded vector and then use these vectors as input to a neural network to forecast the sentiment of the sentence.

Suppose we have a small corpus of text that contains three sentences:

• Each word in these phrases should be represented as a single compressed vector. The first stage is to determine the categorical variable, which is the phrases’ terms. The second stage is to count the number of distinct words in the sentences to calculate the number of potential groups. In this instance, there are 17 potential categories.
• The third stage is to make a binary vector for each of the categories. Because there are 17 potential groups, each binary vector will be 17 bytes long. For example, the binary vector for the word “quick” will be [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], with the 1s in the first and sixth places because “quick” is both the first and sixth group in the list of unique words.
• Finally, we use the binary vectors generated in step 3 to symbolize each word in the sentences as a one-hot encoded vector. For example, the one-hot encoded vector for the word “quick” in the first sentence is [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], and the one-hot encoded vector for the word “seashells” in the second sentence is [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0].

Python Implementation for One-Hot Encoding in NLP

Now let’s try to implement the above example using Python. Because finally, we will have to perform this programmatically else it won’t be possible for us to use this technique to train NLP models.

As you can see from the output, each word in the first sentence has been represented as a one-hot encoded vector of length 17, which corresponds to the number of unique words in the corpus. The one-hot encoded vector for the word “quick” is [0. 0. 0. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 0. 1.].

Assume we have a text collection that includes three sentences:

• Each word in these phrases should be represented as a single compressed vector. We begin by identifying the categorical variable (the words in the sentences) and determining the number of potential groups (the number of distinct words in the sentences), which is 7 in this instance.
• Following that, we generate a binary array with a length of 7 for each group. Because “cat” is the first category in the collection of unique terms, the binary vector for the word will be [1, 0, 0, 0, 0, 0, 0].
• Finally, we use the binary vectors generated in the previous stage to symbolize each word in the sentences as a one-hot encoded vector. For example, in the first sentence, the one-hot encoded vector for the word “mat” is [0, 0, 0, 0, 0, 1], and in the second sentence, the one-hot encoded vector for the word “dog” is [0, 0, 1, 0, 0, 0].

This code initially generates a collection of unique words from the corpus, followed by a dictionary that translates each word into a number. It then iterates through the corpus, creating a binary vector with a 1 at the place corresponding to the word’s integer mapping and a 0 elsewhere for each word in each phrase. The resultant one-hot encoded vectors are displayed for each word in each phrase.

As can be seen, each word is represented as a one-hot encoded vector of length equal to the number of distinct words in the corpus. (which is 7 in this case). Each vector has a 1 in the place corresponding to the word’s integer mapping in the vocabulary set, and a 0 elsewhere.

Drawbacks of One-Hot Encoding in NLP

One of the major disadvantages of one-hot encoding in NLP is that it produces high-dimensional sparse vectors that can be extremely costly to process. This is due to the fact that one-hot encoding generates a distinct binary vector for each unique word in the text, resulting in a very big feature space. Furthermore, because one-hot encoding does not catch the semantic connections between words, machine-learning models that use these vectors as input may perform poorly. As a result, other encoding methods, such as word embeddings, are frequently used in NLP jobs. Word embeddings convert words into low-dimensional dense vectors that record meaningful connections between words, making them more useful for many NLP tasks.

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German launch provider Rocket Factory Augsburg has announced that an RFA ONE first stage, which was to be used for the rocket’s inaugural flight, was destroyed during a hot fire test

In an official statement published late on 19 August, the company revealed that it had attempted a hot fire test of the RFA ONE first stage that evening on its launch pad at SaxaVord Spaceport in Scotland. The statement simply stated that “an anomaly” had led to the loss of the stage.

Additional details regarding the anomaly that led to the loss of the stage were revealed in a short clip shared by the BBC. In the footage, it appears that a fuel leak occurs, eventually causing the entire stage to go up in flames. According to the RFA statement, despite the complete loss of the stage, the launch pad, which was still under construction, was “saved.”

RFA will now work with officials from SaxaVord Spaceport and the relevant UK authorities to analyze what happened, with the goal of returning to regular operations as soon as possible.

In its statement, RFA acknowledged that its iterative approach to vehicle development, with an emphasis on real testing, does come with “higher risks.” The loss of a stage that was to be used for a launch that was potentially weeks away will, however, be a hard pill to swallow.

RFA ONE development costs

According to the company’s most recent financial filings, the development of the RFA ONE rocket and the launch of its inaugural flight had an expected budget of around €90 million. While the filings cover a period up until the end of 2022, it does include a projection that 79% of the €90 million budget would have been utilized by the end of 2023.

With the company now having to build a new first stage equipped with nine of its Helix rocket engines, the expected budget of €90 million will balloon slightly at the very least. The company will also need to redouble its funding efforts to account for the increased development budget.

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Toronto Blue Jays Get Positive Injury Update on Ailing Superstar

Brady farkas | aug 16, 2024.

• Toronto Blue Jays

The Toronto Blue Jays, who are headed for a last-place finish in the American League East, have gotten some good injury news on Friday with regards to shortstop Bo Bichette.

According to Keegan Matheson of MLB.com, Bichette has resumed baseball activities down in Florida.

Bo Bichette has started to do some baseball activities down in Dunedin, John Schneider says. He’ll likely ramp up down in Florida for a while, then check back in with the to evaluate a rehab assignment when it gets to that point.

Bo Bichette has started to do some baseball activities down in Dunedin, John Schneider says. He’ll likely ramp up down in Florida for a while, then check back in with the #BlueJays to evaluate a rehab assignment when it gets to that point. — Keegan Matheson (@KeeganMatheson) August 16, 2024

Bichette has been out since just after the All-Star break with an injured calf muscle, and the hope is that he'll be able to return before the end of the regular season.

It's been a terrible year across the board for Bichette, who is hitting just .223 with four homers and 30 RBI. He's been injured multiple times and hasn't been able to pair with Vladimir Guerrero Jr. to make the kind of dynamic lineup duo that the Blue Jays want to have. There are rumors that Bichette isn't committed long-term to Toronto, and thus, there are rumors that the Jays could trade him in the offseason or at next trade deadline.

In addition to Bichette, closer Jordan Romano is also currently out for the Jays. He underwent elbow surgery and is also trying to make it back before the end of the year, but his timeline is more unclear.

The Blue Jays will play the Cubs again on Saturday and Sunday at Wrigley Field.

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BRADY FARKAS

Brady Farkas is a baseball writer for Fastball on Sports Illustrated/FanNation and the host of 'The Payoff Pitch' podcast which can be found on Apple Podcasts and Spotify. Videos on baseball also posted to YouTube. Brady has spent nearly a decade in sports talk radio and is a graduate of Oswego State University. You can follow him on Twitter @WDEVRadioBrady. 

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Angels Designate Jose Cisnero For Assignment

By Nick Deeds | August 18, 2024 at 1:09pm CDT

The Angels announced this afternoon that they’ve designated right-hander Jose Cisnero for assignment. The move opens up an active roster spot for right-hander Victor Mederos , who was recalled to the majors in a corresponding move. The club also announced that infielder Luis Guillorme , who was designated for assignment earlier this week, has been released.

Cisnero, 35, made his big league debut back in 2013 with the Astros and struggled over parts of two seasons in Houston, with a 4.66 ERA in 48 1/3 innings of work. That would be the journeyman’s only big league action for several years, as the right-hander bounced around various minor league affiliates and independent leagues from 2015 to 2018 before landing with the Tigers in 2019. The then-30-year-old righty impressed in 40 innings of work at the Triple-A level with a 2.70 ERA and a 27.7% strikeout rate, earning him another crack at the big leagues.

The right-hander ultimately spent the next five seasons pitching for the Tigers as a solid, reliable middle relief option. He posted a 3.89 ERA (114 ERA+) with a 4.09 FIP overall, and was particularly impressive from 2020-22 when he pitched to a 2.94 ERA with a 3.65 FIP in 116 1/3 innings of work. Unfortunately, the wheels started to come off for Cisnero last year when he posted a 5.31 ERA with a 4.60 FIP in 63 appearances for the Tigers. Those struggles came in spite of strong strikeout (26.2%) and walk (9.4%) rates that solidly outperformed not only his career numbers, but the numbers he had posted while pitching so effectively for the club in previous years. With strong peripherals, including a 3.73 SIERA and a 4.20 xFIP, suggesting better days ahead, the Angels took a one-year flier on Cisnero’s services this past offseason.

Unfortunately, that experiment did not pay off. Cisnero’s 2024 campaign has been nothing short of brutal as he’s been lit up to a 6.89 ERA with a 6.24 FIP thanks primarily to the fact that he’s allowed four home runs in just 15 2/3 innings of work. The right-hander was sidelined for three months by a bout of shoulder inflammation and made his return to the mound just yesterday, but surrendered two runs (one earned) in 1 2/3 innings of work that saw him allow a hit, a walk, and hit a batter while striking out just one of the eight opponents he faced. That was evidently enough for the Angels to decide to pull the plug on the right-hander, who will now be available for any club in the league to claim off waivers if they so choose.

Taking Cisnero’s place on the Halos’ active roster is Mederos, who has not yet pitched in the majors this year. The right-hander struggled in a brief cup of coffee in the majors last year with a 9.00 ERA in three appearances and hasn’t fared much better in 21 starts split between the High-A and Double-A levels this year, with a 6.56 ERA and a 16.7% strikeout rate in 94 2/3 innings of work. As for Guillorme, the veteran of seven MLB seasons posted a .231/.302/.298 slash line in 50 games for the Angels this year after being acquired from the Braves in an early-season trade. He’ll turn to the free agent market in search of greener pastures, and it’s not hard to imagine a team in need of infield depth having interest in the 29-year-old’s services given his strong defensive reputation and left-handed bat.

23 hours ago

Round two for Mederos. It’s not like he’s an upgrade from Cisnero, just keeping bullpen arms fresh, I’m guessing.

22 hours ago

Mederos just doesn’t get outs consistently. There are 7-10 others guys that deserve his 40 man spot way more. Guess the Angels front office think his “stuff” will get mlb hitters out when his minor league competition ate him up…

21 hours ago

Might be seeing if a team takes a bite on him

18 hours ago

The game was over when Cisneros entered.

The fact he’s held onto a roster spot this long shows just how bad this franchise is.

11 hours ago

We are officially tied for last place with the A’s! If you’re gonna stink, you might as well stink worse than the A’s.

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