How many pulses are needed to change the contents of a 8-bit up counter from…

Convert both binary numbers to decimal: 10101100₂ = 172; 00100111₂ = 39.

• Method 1 (modular arithmetic): compute (target − start) mod 256 because this is an 8-bit up counter.

• Calculate (39 − 172) mod 256 = (−133) mod 256 = 123.

• Method 2 (count-to-end then wrap): pulses to reach 255 from 172 = 255 − 172 = 83; one more pulse wraps to 0 = +1; then advance 39 steps to reach 39 = +39. Total = 83 + 1 + 39 = 123.

Answer: 123 pulses.