Question

if we subtract 1000 from 0001 is there overflow? (binary)

Answer 1

2's Complement subtraction:

Overflow occurs in 2's complement if and only if result and subtrahend and result has same sign.

• (+X) - ( -Y) = -Z (result Z and subtrahend Y has same sign -)

• (-X) - (+Y) = + Z (result Z and subtrahend Y has same sign +)

Given,

X = 0001 (0 in MSB indicates positive number and it's value is +1 in decimal)

Y = 1000 (1 in MSB indicates negative number and it's value is -8 in decimal)

Then,

(+X) - (-Y) = X + Y

Overflow occurs if  result (MSB) and Y has same sign.

MSB of result is 1 which indicates negative number and subtrahend Y has also has the same sign. So therefore there is an overflow.

OR

Since MSB = 1 and carryout = 0 there is an overflow.

Therefore, there is an overflow if we subtract 1000 from 0001.