Subtracting unsigned binary numbers using two methods

[Fatima Hasan]

Homework Statement

Using 8 bit representation , subtract the unsigned binary numbers shown by each of the following methods ;
10101₂ - 1011₂
1) Binary subtraction
2) 2's complement

Homework Equations

-

The Attempt at a Solution

Using binary subtraction :
10101₂ - 1011₂ = 0000 1010₂
Using 2's complement :
10101₂ + ( - 1011₂ )
1011₂ → 1's complement = 0100₂
0100₂ +1 = 0101₂
10101₂ + 101₂ = 0001 1010₂

I didn't get the same answer , can anyone tell me where is my mistake ?

 

[RPinPA]

Using 8 bit representation...

Your 8-bit 2's complement representation of -0000 1011 should have 8 bits. That representation is NOT 0000 0101.

 

[Fatima Hasan]

Your 8-bit 2's complement representation of -0000 1011 should have 8 bits. That representation is NOT 0000 0101.

0000 1011 → 1's complement = 1111 0100
2's complement = 1111 0100 + 1 = 1111 0101₂

 

[RPinPA]

So this is what you had:

$10101_2 + 0101_2$

OK, so now you know that second number should be 1111 0101. And your first number is 0001 0101.

What happens when you add 1111 0101 and 0001 0101 in 8-bit arithmetic?

 

[Fatima Hasan]

OK, so now you know that second number should be 1111 0101. And your first number is 0001 0101.

What happens when you add 1111 0101 and 0001 0101 in 8-bit arithmetic?

11111 0101 + 0001 0101 = 1 0000 1010 = 0000 1010₂