The binary equivalent of 74 is...

The binary equivalent of 74 is...

• A. 1001010
• B. 111010
• C. 0101110
• D. 00100110

Answer: (A)

Expressing a decimal number as binary means marking which powers of two sum to that number. For 74, the largest power of two not exceeding it is 64 (2^6). Subtracting 64 leaves 10, which can be formed as 8 (2^3) plus 2 (2^1). So 74 = 2^6 + 2^3 + 2^1. Placing 1s in those power-of-two positions and 0s elsewhere from 2^6 down to 2^0 gives 1 0 0 1 0 1 0, i.e., 1001010. The other options correspond to 58, 46, and 38, so they aren’t correct.

Expressing a decimal number as binary means marking which powers of two sum to that number. For 74, the largest power of two not exceeding it is 64 (2^6). Subtracting 64 leaves 10, which can be formed as 8 (2^3) plus 2 (2^1). So 74 = 2^6 + 2^3 + 2^1. Placing 1s in those power-of-two positions and 0s elsewhere from 2^6 down to 2^0 gives 1 0 0 1 0 1 0, i.e., 1001010. The other options correspond to 58, 46, and 38, so they aren’t correct.