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

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: \[ {(C)} \]