In the Binary Coded Decimal BCD system we represent decimal numbers in a binary format The format uses 4 bits per decimal digit to encode the numbers 0 through 9 For example the number 971 would be represented in BCD as 9 7 1 |1001|0111|0001|

To convert a BCD number to a binary number we need to do some multiplications by powers of 10 First we split the input vector into parts of width 4 then compute We can do something a little more efficient by starting with the top most digit and computing 9*100 7*10 1 9*10 7 * 10 1

We start by figuring out how many digits we need to process and a counter from is created An accumulator is also created wide enough to hold the largest result value An assertion is raised if num_digits is equal to 1 This is because the register has width which you aren t allowed to do It is not unusual for otherwise generic hardcaml circuit generators to fall down on the smallest example in this way though it often tends to be a trivial case here the circuit literally does nothing if there is only 1 digit and can often be worked around While is 0 we are waiting for to be raised Then for cycles we will add each digit starting from the top most to When we have computed the result and set back to 0 let create clock start bcd let spec Reg_spec create clock in * Find the number of digits to convert and create a counter * let digits split_msb part_width 4 bcd in let num_digits List length digits in * We only support multiple digits for a single digit the output equals the input anyway * assert num_digits > 1 let count Always Variable reg spec width Int ceil_log2 num_digits in * Create an accumulator large enough to hold the final result * let max_result Int pow 10 num_digits 1 in let acc Always Variable reg spec width num_bits_to_represent max_result in * Select the current digit being processed Note that when we split bcd into digits we did so from the top most digit * let digit mux count value digits |> uresize width width acc value in Always compile if_ count value 0 * Wait for start When applied set the accumulator with the top most digit * when_ start count < count value 1 acc < digit * Add each succesive digit to the accumulator times 10 * count < count value 1 acc < drop_top acc value * of_unsigned_int width 4 10 width 4 digit * Finished processing digits * when_ count value num_digits 1 count < 0 acc value count value 0 0 num_digits 1 count Int ceil_log2 num_digits 0 count start num_digits acc * 10 count num_digits 1 count

The following steps are performed Create the BCD design Create a Create a simulator Get the simulator ports Return a function which performs a single test start the circuit with a BCD value wait for it to complete and return the result The function doesn t actually compute a BCD but it does do all the setup stuff which can be time consuming for larger designs It returns a function that allows us to run multiple conversions one after the other let bcd_of_string v String to_list v |> List map f fun c > Char to_int c Char to_int 0 |> Bits of_unsigned_int width 4 |> Bits concat_msb let test num_digits * Create the simulator * let sim let result done_ create clock input clock 1 start input start 1 bcd input bcd num_digits * 4 in Circuit create_exn name bcd output result result output done done_ |> Cyclesim create in * Query the input and output ports * let start Cyclesim in_port sim start in let bcd Cyclesim in_port sim bcd in let done_ Cyclesim out_port sim done in let result Cyclesim out_port sim result in * Start the circuit running and wait for it to be done Return the computed result * let run v start Bits vdd bcd bcd_of_string v Cyclesim cycle sim start Bits gnd Cyclesim cycle sim while not Bits to_bool done_ do Cyclesim cycle sim done Bits to_unsigned_int result in run Circuit Cyclesim test

let%expect_test let run test 5 in Stdio print_s %message run 00000 int Stdio print_s %message run 12345 int Stdio print_s %message run 99999 int %expect | run 00000 0 run 12345 12345 run 99999 99999 | let run test 2 in Stdio print_s %message run 00 int Stdio print_s %message run 21 int Stdio print_s %message run 55 int Stdio print_s %message run 99 int %expect | run 00 0 run 21 21 run 55 55 run 99 99 |