[Solved] Consider a computer that uses 5 bits to represent integers using – Computer Science

Answer

In a 5-bit integer representation where 1 bit is used for the sign and 4 bits for the value, the maximum positive integer that can be represented is +15 (when the 4 bits are all 1s) and the minimum negative integer is -16 (when the sign bit is 1 and the value bits are all 0s).

An integer overflow occurs when an arithmetic operation attempts to create a numeric value that is outside of the range that can be represented with a given number of bits.

Given this, let’s evaluate each of the options:

Choice A: 7 + 1

This operation results in 8, which is within the representable range. So, this operation does not cause an overflow.

Choice B: 6 + 9

This operation results in 15, which is within the representable range. So, this operation does not cause an overflow.

Choice C: 1 + 15

This operation results in 16, which is outside the representable range. So, this operation does cause an overflow.

Choice D: 12 + 3

This operation results in 15, which is within the representable range. So, this operation does not cause an overflow.

Choice E: 8 x 2

This operation results in 16, which is outside the representable range. So, this operation does cause an overflow.

Choice F: 2 x 4

This operation results in 8, which is within the representable range. So, this operation does not cause an overflow.

So, the operations that would result in integer overflow are Choice C: 1 + 15 and Choice E: 8 x 2.