Which binary representation is correct for the number 5?

Which binary representation is correct for the number 5?

• A. 1010
• B. 0000
• C. 0011
• D. 0101

Answer: (D)

Binary uses powers of two. To represent 5, pick the largest power of two not exceeding 5, which is 4 (2^2). Subtracting 4 from 5 leaves 1, which is 2^0. So the bits for the four places (2^3, 2^2, 2^1, 2^0) are 0, 1, 0, 1, giving 0101. This corresponds to 0·8 + 1·4 + 0·2 + 1·1 = 5. The other patterns map to 10, 0, and 3 respectively, so 0101 is the correct binary representation for 5.

Binary uses powers of two. To represent 5, pick the largest power of two not exceeding 5, which is 4 (2^2). Subtracting 4 from 5 leaves 1, which is 2^0. So the bits for the four places (2^3, 2^2, 2^1, 2^0) are 0, 1, 0, 1, giving 0101. This corresponds to 0·8 + 1·4 + 0·2 + 1·1 = 5. The other patterns map to 10, 0, and 3 respectively, so 0101 is the correct binary representation for 5.