What is the 7-bit binary representation of the decimal number 74?

What is the 7-bit binary representation of the decimal number 74?

• A. 1001010
• B. 1001001
• C. 01001010
• D. 1101010

Answer: (A)

To represent a decimal number in binary, you break it down into sums of powers of two. For a 7-bit representation, the leftmost bit is 2^6 (which is 64), then 2^5 (32), down to 2^0 (1). Decompose 74 as 64 + 8 + 2. That means the bits are 1 for 2^6, 0 for 2^5, 0 for 2^4, 1 for 2^3, 0 for 2^2, 1 for 2^1, and 0 for 2^0. Writing these from left to right gives 1001010. The other patterns don’t fit: 1001001 would be 64 + 8 + 1 = 73; 01001010 is an 8-bit representation (leading zero included), not the 7-bit form requested; and 1101010 equals 106.

To represent a decimal number in binary, you break it down into sums of powers of two. For a 7-bit representation, the leftmost bit is 2^6 (which is 64), then 2^5 (32), down to 2^0 (1). Decompose 74 as 64 + 8 + 2. That means the bits are 1 for 2^6, 0 for 2^5, 0 for 2^4, 1 for 2^3, 0 for 2^2, 1 for 2^1, and 0 for 2^0. Writing these from left to right gives 1001010. The other patterns don’t fit: 1001001 would be 64 + 8 + 1 = 73; 01001010 is an 8-bit representation (leading zero included), not the 7-bit form requested; and 1101010 equals 106.