Question

Arrange the following steps in correct order to binary:
• [(i)] Repeat division until becomes 0
• [(ii)] Divide the number by 2
• [(iii)] Write the remainder
• [(iv)] Write the remainder in reverse order

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

Hint:

For decimal-to-binary conversion always remember: \[ \text{Divide} \rightarrow \text{Write Remainder} \rightarrow \text{Repeat} \rightarrow \text{Reverse} \] This simple sequence helps in solving conversion questions quickly.

Answer 1

The Correct Option is B

Concept: Decimal-to-binary conversion follows a systematic algorithm based on repeated division by 2. Every step must be performed in a specific order to obtain the correct binary representation.

Step 1: Identify the first operation. The process begins by dividing the decimal number by 2. Therefore, the first step is: \[ (ii) \]

Step 2: Record the remainder. After every division, the remainder must be noted because it becomes part of the binary representation. Therefore, the second step is: \[ (iii) \]

Step 3: Continue the process. The quotient obtained from the division is again divided by 2. This procedure is repeated until the quotient becomes zero. Therefore, the third step is: \[ (i) \]

Step 4: Construct the binary number. The remainders are generated from least significant bit to most significant bit. To obtain the final binary number, the remainders are written in reverse order. Therefore, the final step is: \[ (iv) \]

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