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How to convert a binary number to its equivalent BCD?
In this lecture, 
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I will explain a straightforward algorithm to design a digital circuit performing this conversion. 
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So designing a combinational circuit to encode a binary number into the BCD is our goal here..
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A simple C function can do this encoding process by extracting each digit in a while-loop, as shown in this 
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code.
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Line 4 in this code finds a least significant digit in the binary number using the modulo 10 
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operation, and line 5 modifies the binary number and prepare that for the next iteration.
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Let’s take an example and follow the code. 
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If we assume, the binary number is 0b11101011 = 235 
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in decimal then the first iteration of this code extracts the first digit into bcd[0] and replaces 
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the binary number with 23. 
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The second and third iterations find the 3 and 2 digits, respectively. 
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Let’s modify the binary2bcd C function to be synthesised by Vivado-HLS for the Basys3 board. 
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First of all, the while-loop instruction implicitly implies a kind of sequentially ordered execution 
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which means its implementation requires temporary memories which is against the combinational circuit 
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definition.
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Although, in the next section, I will explain the combinational-loops and the techniques that we use to 
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implement a software loop with combinational circuits. 
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But, until that time, we should get rid of the loop statement.
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As we are considering the Basys3 board and it has only four 7segments, it is practical to 
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consider only 4-digit BCD numbers in our binary to BCD algorithm. 
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In this case, the input number would be between 0 and 9999. 
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So, we need at most 16 bits to save the final BCD code and 14 bits for the equivalent binary code.
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Before modifying the C function, let’s define a few arbitrary precision unsigned integer data types.
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We need a 14-bit data type to get the input binary number, 16-bit data type to send out the BCD code 
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for four 7segments and 4-bit data type to represent a single BCD digit inside the code. 
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The body of the while-loop in the previous C function has two main mathematical calculations, 
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let’s put them in a sub-function and call the sub-function four times corresponding to the four-digit BCD 
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output.
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Notice that the Vivado-HLS implements the modulus operator with Xilinx LogiCORE divider IP which 
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generally is not a combinational circuit. 
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Therefore, we replace that with the equivalent expression, which is commented out in our original C 
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function.
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So, the get_digit function, as shown here, will be synthesised into a combinational circuit by
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Vivado-HLS toolset. 
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Now, let’s write the HLS top- function. The top-function gets a 14-bit binary number via the in_binary variable 
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and returns 4-digit packed BCD through a 16-bit pointer variable named packed_bcd. 
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Inside the function body, let’s define a 14-bit variable to save the input binary value throughout 
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the algorithm. 
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Also, we need to define four 4-bit variables to keep the 4 BCD digits. 
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Now, we call the get_digit sub-function four times to extract the four BCD digits. 
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Then, the four extracted BCD should be concatenated into the output variable. 
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Finally, we should define the function argument interfaces and the function block interface.
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The HLS C code explained here uses some arithmetic operations such as division and addition. 
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However, a more efficient algorithm that only uses shift and add operators can be used to convert a 
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binary number into the BCD code. 
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This algorithm is called Dobble-Dabble, 
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that is explained in the next lecture.
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These are our takeaway messages.  HLS synthesises the integer and arbitrary-precision data type 
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arithmetic operators into a combinational circuit except for the modulus operator.
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HLS implements the modulus operator with the Xilinx LogiCORE divider IP which is not generally 
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a combinational circuit.
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Now the quiz for this lecture. Synthesis the C function “binary2bcd_div” explained earlier in 
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this lecture using HLS and report the resource utilisation.