The problem asks to find the two's complement representation of the numbers 56 and -56 using 8 bits.

1. Problem Description

The problem asks to find the two's complement representation of the numbers 56 and -56 using 8 bits.

2. Solution Steps

i) For 56:

First, find the binary representation of the absolute value of the number,

5

6. The process in the image is correct, but needs completion to arrive to the final result.

$56 / 2 = 28$ remainder $0$

$28 / 2 = 14$ remainder $0$

$14 / 2 = 7$ remainder $0$

$7 / 2 = 3$ remainder $1$

$3 / 2 = 1$ remainder $1$

$1 / 2 = 0$ remainder $1$

Reading the remainders from bottom to top, we get the binary representation: $111000$.

Since we need an 8-bit representation, we pad with leading zeros: $00111000$. Because 56 is positive, its two's complement representation is the same as its binary representation.

ii) For -56:

1. Find the binary representation of the absolute value of the number, 56, as we found in the previous step. This is $00111000$.

2. Find the one's complement by inverting all the bits (0s become 1s and 1s become 0s).

So, $00111000$ becomes $11000111$.

3. Find the two's complement by adding 1 to the one's complement.

$11000111 + 1 = 11001000$

3. Final Answer

i) The two's complement representation of 56 is

0

0

1

1

1

0

0

0. ii) The two's complement representation of -56 is 11001000.