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Transforming the data format is one of the common tasks in digital design.  
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This lecture will explain how to describe these transformations in HLS.
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Encoder and Decoder circuits are combinational logics that transform the shape of their received data. 
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They transform data from one format to another.  An encoder usually transforms the original data format 
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into a coded format for different reasons such as security, compression, transmission, error-prone 
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safety, to name a few. 
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A decoder usually performs the reverse function and transforms a coded data format into the original 
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data format.  A classical encoder/decoder receives n-bit input data and generates m-bit output
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data.
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Let’s take an example and clarify the concept of encoder and decoder. Our examples in this slide and 
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the next slide is octal to binary encoder/decoder. 
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The octal to binary encoder consists of eight inputs and three outputs. Each input corresponds to an octal digit,
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and three outputs represent the corresponding binary code.
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It is to be assumed that only one input is active or has the value of 1 at any given time; 
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otherwise, the circuit has no meaning. 
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For example, if input (D7, D6, D5, D4, D3, D2, D1, D0) is (0,0,0,1,0,0,0,0) then the output will be (Y2, Y1, Y0) = 100.
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And the input (0,0,0,1,0,0,1,0) is not possible 
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as two input lines are 1.
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The octal decoder performs the reverse function. It has three inputs and eight outputs. It receives a 3-bit 
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binary code and activates the corresponding octal output.
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For example, if the inputs are 010 then the outputs are  00000100.
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00000100.
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A classic general binary encoder in digital design is a combinational circuit that receives 
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the maximum of 2 to the nth power binary inputs and generates n binary outputs. Its role in the logic design 
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is encoding a given input and provide an encoded output which is the compact form of the input. 
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This table describes a 4 by 2 binary encoder.
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In this encoder, only one of the inputs can be 1 and others must be 0.  As it can be seen, 
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the output is the binary value of the position index of the only one in the inputs. 
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A classic general binary decoder in digital design is a combinational circuit that receives the maximum 
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of n binary inputs and generates 2 to the nth power binary outputs. 
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Its role in the logic design is decoding a given coded data and provides the original data. 
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This table describes a 2 by 4 binary decoder. As can be seen, only one of the outputs is 1 and 
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rests are 0.
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Also, the binary input represents the position index of the 1 in the outputs.
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The switch case programming structure in HLS code can be used to describe the binary encoders 
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and decoders. For example, let's consider this 2 by 4 binary decoder, 
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then this function containing a switch statement represents this decoder.  
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Each case in the switch statement determines one possible output value corresponding to the input 
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values.
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In other words, each case represents one row of the left-hand side table.
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A typical HLS tool synthesises a switch case with multiplexers. 
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If we consider the 2 by 4 decoder shown in the previous slide, then a 4 by 1 multiplexer can 
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implement the switch-case representation.
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Now that we have understood how to describe a classic encoder/decoder in HLS software, the next lecture 
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will describe more detains on using the switch-case software statement to describe similar ideas by taking 
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an example called leading one.
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These are our takeaway messages. Encoder and decoder are hardware circuits to change a data format.
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The switch-case statement in HLS code can represent a typical encoder/decoder circuit.
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Now the quiz question. Use a switch-case statement in HLS to describe an 8 by 3 encoder circuit.