Question

Which of the following is the representation of decimal number (- 147) in 2’s compliment notation on a 12-bit machine ?
1. 111101101100
2. 110001001101
3. 111101101101
4. 000001101101

Answer 1

Correct Answer - Option 3 : 111101101101

The Correct Answer is 111101101101.

• Conversion of  (-147) to a signed binary in 2's complement representation:
• The positive version of the number: |-147| = 147
• Divide the number repeatedly by 2 to get the binary form of (147): We stop when we get a quotient that is equal to zero.
• We will get the binary number: 147₍₁₀₎ = 10010011₍₂₎
• The Positive binary computer representation on 16 bits (2 Bytes): Add extra 0's in front (to the left) of the base 2 number, up to the required length, 16: 147₍₁₀₎ = 0000000010010011
• Get the negative integer number representation on 16 bits: !(0000000010010011) = 1111111101101100
• To get the negative integer number representation on 16 bits (2 Bytes), the signed binary two's complement, add 1 to the number calculated above: 1111111101101100 + 1 = 1111111101101101
• -147₍₁₀₎ = 1111111101101101