Question

Give the formulas for the minimum and maximum values representable in n bits for:

(a) unsigned

(b) signed magnitude

(c) two’s complement

(d) one’s complement

Answer 1

A. For unsigned numbers,

minimum value = 0

maximum value = 2ⁿ-1

For example for 5 bits range will be 0 to 31. 31 in binary 11111 that is max number possible using 5 bits.

B. For signed numbers,

minimum value =  -(2^(n-1)-1)

maximum value = (2^(n-1)-1)

For example, for 6 bits -(2⁵-1) to (2⁵-1) means -31 to +31.

C. For two's complement,

minimum value =  -(2^(n-1))

maximum value = (2^(n-1)-1)

For example, for 6 bits, range will be -(2⁵) to (2⁵-1) means -32 to +31.

C. For one's complement,

minimum value =  -(2^(n-1)-1)

maximum value = (2^(n-1)-1)

For example, for 6 bits -(2⁵-1) to (2⁵-1) means -31 to +31.