Question

The decimal equivalent of hexadecimal 3AF is:

• A. 933
• B. 943
• C. 953
• D. 963

Hint:

Always remember the "F" value is 15. A quick check: $16^2$ is 256, and $3 \times 256$ is 768. Since $A$ is 160, the answer must be above 928, which narrow choices down.

Answer 1

The Correct Option is B

Concept: To convert a hexadecimal number (base-16) to a decimal number (base-10), we multiply each digit by 16 raised to the power of its position index (starting from 0 on the right).

Step 1: Assign values to Hexadecimal characters.
In Hex: $A = 10, B = 11, C = 12, D = 13, E = 14, F = 15$. For $3AF$: - $3 = 3$ - $A = 10$ - $F = 15$

Step 2: Apply positional weights.
Index positions for $3AF$: - $F$ is at index $0$ ($16^0$) - $A$ is at index $1$ ($16^1$) - $3$ is at index $2$ ($16^2$)

Step 3: Perform the calculation.
Decimal $= (3 \times 16^2) + (10 \times 16^1) + (15 \times 16^0)$ Decimal $= (3 \times 256) + (10 \times 16) + (15 \times 1)$ Decimal $= 768 + 160 + 15$ Decimal $= 943$.