Which one of the following represents the binary equivalent of the decimal…

Concept — A binary numeral is a sum of powers of two: the digit standing k places from the right is a coefficient of the place value 2k. A five-bit string b4 b3 b2 b1 b0 therefore denotes b4·24 + b3·23 + b2·22 + b1·21 + b0·20. Converting the other way — decimal to binary — uses the repeated-division rule: divide the decimal number by 2 again and again, keep the remainder at every step, and read those remainders from the last division back to the first.

Application — Apply the repeated-division rule to the decimal number 23:

1. 23 ÷ 2 = 11, remainder 1

2. 11 ÷ 2 = 5, remainder 1

3. 5 ÷ 2 = 2, remainder 1

4. 2 ÷ 2 = 1, remainder 0

5. 1 ÷ 2 = 0, remainder 1

Reading the five remainders from the last division back to the first gives 1, 0, 1, 1, 1 — that is, the string 10111.

Cross-check — Expand 10111 by place value: 1·24 + 0·23 + 1·22 + 1·21 + 1·20 = 16 + 0 + 4 + 2 + 1 = 23. The polynomial expansion returns the number we started from, so the conversion is confirmed: the binary equivalent of decimal 23 is 10111.

Contrast — The other five-bit strings offered expand to different decimal values, which is why they do not answer the question:

Because one of the listed five-bit strings does expand to 23, the "None of the above" choice does not apply here.