Question

Arrange the steps to find two's complement of a binary number:
• [(i)] Take 1's complement
• [(ii)] Write the binary number
• [(iii)] Add 1
• [(iv)] Obtain final result

• A. (iv) $\rightarrow$ (i) $\rightarrow$ (iii) $\rightarrow$ (ii)
• B. (ii) $\rightarrow$ (iii) $\rightarrow$ (i) $\rightarrow$ (iv)
• C. (ii) $\rightarrow$ (i) $\rightarrow$ (iii) $\rightarrow$ (iv)
• D. (i) $\rightarrow$ (ii) $\rightarrow$ (iii) $\rightarrow$ (iv)

Hint:

To find a two's complement quickly:
• Write the binary number.
• Invert all bits.
• Add 1. This shortcut always produces the correct two's complement representation.

Answer 1

The Correct Option is C

Concept: Two's complement is the most widely used method for representing signed binary numbers in computers. It allows both positive and negative integers to be represented using the same binary arithmetic circuitry. The fundamental rule is: \[ \text{Two's Complement} = \text{One's Complement} + 1 \] To obtain the two's complement of a binary number, a specific sequence of operations must be followed.

Step 1: Write the original binary number. Before performing any operation, the given binary number must be written. This corresponds to: \[ (ii) \]

Step 2: Find the 1's complement. The next step is to invert every bit. \[ 0 \rightarrow 1 \] \[ 1 \rightarrow 0 \] This operation produces the 1's complement. This corresponds to: \[ (i) \]

Step 3: Add 1 to the result. After obtaining the 1's complement, add binary 1. This converts the 1's complement into the 2's complement. This corresponds to: \[ (iii) \]

Step 4: Obtain the final result. The binary number obtained after addition is the required two's complement. This corresponds to: \[ (iv) \]

Step 5: Writing the correct sequence. Thus, the complete order is: \[ (ii) \rightarrow (i) \rightarrow (iii) \rightarrow (iv) \] Hence, the correct answer is: \[ \boxed{(C)} \]