What is the binary representation of the decimal number 0.25 ?

Concept: To convert a decimal fraction to binary, express it as a sum of negative powers of 2 - the first digit after the binary point carries weight 2-1, the second 2-2, the third 2-3, and so on, mirroring how whole-number binary digits carry weights 20, 21, 22 ...

1. Multiply the fraction by 2: 0.25 × 2 = 0.50. The integer part is 0, so the first digit after the binary point is 0; the remaining fraction 0.50 is carried forward.

2. Multiply the remaining fraction by 2 again: 0.50 × 2 = 1.00. The integer part is 1, so the second digit is 1; the remaining fraction is now 0, so the conversion stops.

3. Reading the digits in the order they were generated gives 0.01 in binary.

Cross-check: converting 0.01 back to decimal gives 0 × 2-1 + 1 × 2-2 = 0 + 0.25 = 0.25, which matches the original number, confirming the conversion.