The problem asks to represent the numbers 26 and -34 in binary using 8 bits, where the most significant bit (MSB) represents the sign.

1. Problem Description

The problem asks to represent the numbers 26 and -34 in binary using 8 bits, where the most significant bit (MSB) represents the sign.

2. Solution Steps

i) Representing 26:

Since 26 is a positive number, the sign bit will be

0. We need to represent 26 in binary using the remaining 7 bits.

$26 = 16 + 8 + 2$

$26 = 2^4 + 2^3 + 2^1$

So, the binary representation of 26 is

0

0

1

1

0

1

0. Since we have 7 bits, we pad it with leading zeros.

Since it is positive, the sign bit is

0. The 8-bit representation will be

0

0

0

1

1

0

1

0.

ii) Representing -34:

Since -34 is a negative number, the sign bit will be

1. We will use the two's complement representation. First, we find the binary representation of

3

4.

$34 = 32 + 2$

$34 = 2^5 + 2^1$

The binary representation of 34 using 7 bits is

0

1

0

0

0

1

0.

To find the two's complement, we first invert the bits:

0100010 becomes 1011101

Then we add 1:

1011101

+ 0000001

= 1011110

Since the number is negative, the sign bit is

1. So, the 8-bit representation is

1

1

0

1

1

1

1

0.

3. Final Answer

i) 00011010

ii) 11011110