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How can we describe a multiplexer in HLS? In this lecture, 
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I am going to introduce three different coding techniques to describe a multiplexer.
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Let’s consider the 2x1 mux defined in the previous lecture. 
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The input a is connected to the output 
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if s=0, otherwise b is transferred to the output.
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Probably, the simplest way to code this mux in C/C++ is using the ternary conditional operator, in which 
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a is copied to O if s equals to 0 otherwise b is copied to O.  
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Another way of coding this 2x1 MUX is by using the if-else statement. Notice that if you
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are going to implement a mux with a conditional if, you should clearly mention both if and else 
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parts.
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Notice that these two conditional if statements may not be synthesised into combinational circuits as 
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they both should keep track of the previous value of the output o.
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The left-hand side if statement does not define the else part, which means if s is not 0, the output 
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should keep its previous value which in some cases it needs a kind of memory in the hardware implementation. 
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The right-hand side if statement has defined the else part, but it says that that output should keep 
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its previous value.
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This if statement also can be synthesised into sequential logic in some cases. 
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Therefore, to make sure that the final implementation is combinational, 
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we should explicitly define all parts in if-else statements.
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Another way of describing a multiplexer in HLS is by using the switch-case statement.  Notice that, 
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there should be an execution path in the switch-case for any possible value of the select input to represent 
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a combinational circuit. 
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In this example, all cases in the switch have been mentioned explicitly. 
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In addition, the sel variable in the code has 2 bits that can directly connect to the MUX in the 
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hardware implementation.
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This code is another example of a combinational multiplexer described by the switch-case statement. 
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The sel variable in the code has 8-bits which means it can define 256 different cases. 
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However, the code only has 4 data inputs that are a, b, c and d. 
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Therefore multiple cases in the switch statement should send the same input to the output. So, the sel 
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cannot directly drive the MUX select input. 
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A selection logic” which is a combinational circuit” should generate the select input for the MUX. 
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Transforming data from one format to another is one of the combinational circuit task. The next lecture 
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will explain the concept of encoder and decoder, the two common combinational circuits transforming  
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data.
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These are our takeaway messages. The software if-then-else statement can be used to implement 
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multiplexers.
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The switch-case statement is another way of describing a multiplexer in HLS. 
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Now the quiz question. Draw the structure of a combinational circuit that can implement this HLS code.