Hexadecimal to decimal conversion — What is the decimal (base-10) value of the hexadecimal number 777 (base 16)?

Introduction:Converting between hexadecimal and decimal is a routine task in digital electronics, debugging, and low-level programming. Understanding positional weights (powers of 16) allows quick mental or written conversion for any hex string, including repeating digits like 777.

Given Data / Assumptions:

• Hex number: 777 (base 16).
• Digit values: 7 in hex equals 7 in decimal.
• Weights: 16^0, 16^1, 16^2 for the three positions.

Concept / Approach:

Use positional expansion: value = d2 * 16^2 + d1 * 16^1 + d0 * 16^0. Each “7” contributes 7 times its place weight. Sum the contributions to obtain the decimal result.

Step-by-Step Solution:

Verification / Alternative check:

As a quick check, note that 0x3FF (1023) is 10 bits set; 0x777 is smaller but in the same ballpark. Exact arithmetic confirms 1911.

Why Other Options Are Wrong:

• 191 / 19 / 19111: Incorrect sums or extra digits.
• 777: Merely restates the hex string, not a base-10 value.

Common Pitfalls:

• Treating hex digits as decimal weights (base-10) instead of base-16 powers.
• Forgetting that A–F represent 10–15 in hex for other problems.

Final Answer:

1911