Question

Show that in 2’s complement binary system, the highest significant position acts like a sign (not the same) as in the signed-magnitude binary system. Is this true for any radix-r number system? Justify your answer.

Answer 1

It is NOT true for any radix-r number system.

For binary number system it is true that highest significant bit acts as sign bit for both signed magnitude representation and 2's complement representation, but it is no true for all. We can prove it by contradiction, in decimal representation signed magnitude form we dont use highest significant bit as sign bit, instead we use '+' / '-' as prefix of the number for signed magnitude representation, hence proved the above statement is not true.