What is the 8-bit binary representation of decimal 25?

• A. 00011001
• B. 00101001
• C. 00011111
• D. 00001001

Answer: (A)

Think in terms of powers of two. Each bit represents a value from left to right: 128, 64, 32, 16, 8, 4, 2, 1. To make decimal 25, use the powers that add up to 25: 16 + 8 + 1. Put 1s in the positions for 16, 8, and 1, and 0s elsewhere. That gives 00011001. Padding to eight bits just adds leading zeros to the normal 5-bit form 11001. If you sum the ones in other patterns, you’d get different totals (for example, a 1 in the 32 or 4 or 2 positions would change the total), so this pattern uniquely represents 25.