Your computer uses 4 bits to represent decimal numbers (0, 1, 2, 3 and so on) in binary. What is the SMALLEST number for which an overflow error occur?

Question

A. 14
B. 15
C. 16
D. 17

Answer 1

To determine the smallest number for which an overflow error occurs using 4 bits in binary representation, we first need to know the maximum value that can be represented with 4 bits:

In binary, 4 bits can represent values from \(0000_2\) (which is 0 in decimal) to \(1111_2\) (which is 15 in decimal). Thus, the range of values is from 0 to 15.

An overflow error occurs when a number exceeds the maximum representable value. Since the highest number that can be represented with 4 bits is 15, the smallest number that causes an overflow is 16.

Therefore, the answer is:

C. 16