Question

1. Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. 01102 + 01002

2.Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. 10102 + 11112

3.Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. 10112 + 01112

Answer 1

Solution:

since there are 4 bits therefore 2's complement can be within the range of (-2^4-1) to (+2^{4 - 1}-1) ie - 8 to +7

so by adding 2 numbers of 2's complement if they go outside that range then they are overflowing .

Hence :-

soln 1.>

Add 0110 + 0100

0110 in 2s complement = +6

0100 in 2s complement = +4

6+4 =+10 which goes outside they range since at max we can go to +7 using 4bits 2s complement notation therefore its an OVERFLOW

soln 2.>

Add 1010 + 1111

1010 in 2s complement = -6

1111 in 2s complement = -1

(-6)+(-1) =-7  which does not goes outside the range since at max we can go to -8 using 4bits 2s complement notation therefore its NO OVERFLOW

soln 3.>

Add 1011 + 0111

1011 in 2s complement = - 5

0111 in 2s complement = +7

-5 +7 =+2  which does not goes outside the range since at max we can go to +7 using 4bits 2s complement notation therefore its NO OVERFLOW

SHORTCUT(for signed notation or 2s complement notation):-