Question

The octal equivalent of Binary 101110010 is:

• A. 562
• B. 762
• C. 572
• D. 772

Hint:

When converting Binary to Octal, always group from right to left. If you have fewer than 3 bits on the left, pad them with leading zeros.

Answer 1

The Correct Option is A

Concept: Octal numbers are base-8. Since $2^3 = 8$, every three binary digits (bits) correspond exactly to one octal digit. This makes the conversion simple: group the bits in threes starting from the right.

Step 1: Group the binary digits.
Binary: $101~110~010$ - Group 1 (Right): $010$ - Group 2 (Middle): $110$ - Group 3 (Left): $101$

Step 2: Convert each group to decimal.
- $101 = (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) = 4 + 0 + 1 = \mathbf{5}$ - $110 = (1 \times 2^2) + (1 \times 2^1) + (0 \times 2^0) = 4 + 2 + 0 = \mathbf{6}$ - $010 = (0 \times 2^2) + (1 \times 2^1) + (0 \times 2^0) = 0 + 2 + 0 = \mathbf{2}$

Step 3: Combine the results.
The resulting digits are $5$, $6$, and $2$. Octal equivalent $= 562_8$.