To find out the greatest negative number that can be stored in a 4-bit binary word that uses 2's compliment arithmetic.The total number of distinct numbers that can be stored in a 4-bit word are 2^4 (including zero) = 16.

But to store negative numbers, these 16 numbers should be such distributed ,so that every positive number has a 2's compliment negative counterpart.But excluding zero there are 15 numbers exclusively.

15 being an odd number cannot be divided in two groups equally.This is where the problem arises.

0000

0001 -> 1111

0010 -> 1110

0011 -> 1101

0100 -> 1100

0101 -> 1011

0110 -> 1010

0111 -> 1001

Here we can see seven positive numbers ,seven negative numbers and zero.The count is 15.

The number omitted is '1000'.

We know that generally, 1000 is considered as -8 and regarded as the greatest negative number that can be stored in a 4-bit word that uses 2's compliment method.

1000, if 2's complimented, gives back 1000.How can we differentiate between +8 and -8 ?

Why is it, that 1000 is always taken as -8 and the greatest positive number that can be stored is 7 and not 8?

And what about the 2's compliment of zero?

This 4-bit problem can be applied to any number of bits.

I hope I could state my problem clearly.Waiting for further discussion...

Thanks in advance.

Koustav Ghosal