Question

What is the 2's complement representation of the decimal number -5 in 8-bit binary?

• A. 00000101
• B. 11111011
• C. 11111010
• D. 00000110

Hint:

Shortcut: To find 2's complement quickly, start from the right side of the positive binary number. Keep all bits the same up to and including the first '1'. Then, flip every bit to the left of that '1'. Example: $0000010[1] \rightarrow 1111101[1]$.

Answer 1

The Correct Option is B

Concept: Two's complement is the standard way to represent signed integers in binary. To find the 2's complement of a negative number, we follow a specific three-step process:
• Find the binary representation of the positive version of the number.
• Find the 1's complement (invert all bits).
• Find the 2's complement (add 1 to the 1's complement).

Step 1: Represent +5 in 8-bit binary.
First, we write the binary for 5, which is $4 + 1$ ($2^2 + 2^0$). In 8-bit format, this is: \[ +5 = 00000101 \]

Step 2: Calculate the 1's complement.
Flip every bit (0 becomes 1, and 1 becomes 0): \[ \text{1's complement of } 5 = 11111010 \]

Step 3: Calculate the 2's complement.
Add 1 to the result of
Step 2: \[ \begin{array}{r@{\quad}l} 11111010 & (\text{1's complement}) + 00000001 & (\text{Add 1}) \hline 11111011 & \end{array} \] The result 11111011 represents -5 in 8-bit 2's complement.