What is the binary representation of 3?

What is the binary representation of 3?

• A. 0101
• B. 0011
• C. 1111
• D. 1000

Answer: (B)

Binary numbers add up as sums of powers of two. The number 3 is 2 + 1, so the bits for 2^1 and 2^0 are 1, and the higher powers are 0. In a 4-bit representation that gives 0 0 1 1, i.e., 0011. The other patterns correspond to 5 (0101), 15 (1111), and 8 (1000), so they don’t represent 3. The key idea is that each bit represents a power of two, and setting the appropriate bits to 1 adds up to the target value.

Binary numbers add up as sums of powers of two. The number 3 is 2 + 1, so the bits for 2^1 and 2^0 are 1, and the higher powers are 0. In a 4-bit representation that gives 0 0 1 1, i.e., 0011. The other patterns correspond to 5 (0101), 15 (1111), and 8 (1000), so they don’t represent 3. The key idea is that each bit represents a power of two, and setting the appropriate bits to 1 adds up to the target value.