Question

A computer with 32 bit word size uses 2s compliment to represent numbers. The range of integers that can be represented by this computer is
1. –2³²  to 2³²
2. –2³¹ to 2³² –1
3. –2³¹ to 2³¹ –1
4. –2³¹ –1 to 2³² –1

Answer 1

Correct Answer - Option 3 : –2³¹ to 2³¹ –1

Data:

number of bits = n = 32

Formula:

Range of 2's compliment number with n bits is (–2n-1 ) to +(2n-1 – 1)

Smallest integer = –2n-1

largest integer = 2n-1 – 1

Calculation:

Smallest integer = –232-1 = –2³¹

Largest integer = 232-1 – 1 =  231 – 1

Range is –231 to 231 –1