The problem asks to find the 8-bit binary representation of the number 26, where one bit is used for the sign. This means that 7 bits are available for the magnitude of the number.

1. Problem Description

The problem asks to find the 8-bit binary representation of the number 26, where one bit is used for the sign. This means that 7 bits are available for the magnitude of the number.

2. Solution Steps

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

0. We need to find the binary representation of 26 using the remaining 7 bits.

The binary representation of 26 can be found by repeatedly dividing by 2 and noting the remainders:

$26 \div 2 = 13$ with remainder 0

$13 \div 2 = 6$ with remainder 1

$6 \div 2 = 3$ with remainder 0

$3 \div 2 = 1$ with remainder 1

$1 \div 2 = 0$ with remainder 1

Reading the remainders from bottom to top gives the binary representation of 26 as

1

1

0

1

0. Since we need 7 bits for the magnitude, we pad the left with zeros to get

0

0

1

1

0

1

0. Finally, we add the sign bit (0 for positive) to the beginning.

So, the 8-bit representation is

0

0

0

1

1

0

1

0.

3. Final Answer

00011010