6 In a 7 bit cell what is the range of values binary and dec

6> In a 7 bit cell what is the range of values, binary and decimal, that can be stored in a signed representation, assuming 2\'s complement?

Solution

In a 7 bit cell, 1 bit is used for sign. So the range of absolute values will be whatever can be stored in 6 bits.

The first bit indicates sign and 0000000 represents 0 So positive integers that can be represented are 2^6 -1 as 1 combination that starts with 0 has been taken to represent 0.

Negative numbers that can be represented are upto -2^6

As 6 bits can be used to represent numbers up to 64, here in 2s complement the range of numbers that can be stored is from -64 to +63 in decimal and

1111111 to 0000000 to 0111111

-64 to 0 to +63

(1st bit is a sign bit here in binary.)

No. of bits	Numbers
1	2	0 or 1
2	4	2^2
3	8	2^3
4	16	2^4
5	32	2^5
6	64	2^6