Observe the following pairs of binary numbers:

00011111 and 00100000

00111111 and 01000000

01111111 and 10000000

Describe the general relationships between these pairs of numbers in terms of:

Decimal values.

Powers of 2.

Number of bits required.

Other relationships ...

These descriptions of relationships should hold for all of these pairs of numbers.

The general relationship between each pair in terms of decimal values, powers of 2 and number of bit required are shown in form of table below:

Binary No. Decimal Value Power of 2 No. of Bits (n) Relation Ship

a=00011111 31 2⁵-1 n=5 b=a+1

b=00100000 32 2⁵ n+1=6

a=00111111 63 2⁶-1 n=6 b=a+1

b=01000000 64 2⁶ n=6+1

a=01111111 127 2⁷-1 n=7 b=a+1

b=10000000 128 2⁷ n+1=8