Hexadecimal to decimal — evaluate the statement: “64 hexadecimal equals 100 decimal.” Treat “64 hexadecimal” as the base-16 number 0x64 and verify its base-10 value.

Introduction / Context:Converting between hexadecimal (base 16) and decimal (base 10) is a routine skill in computer architecture, low-level programming, and digital electronics. This question asks you to verify whether the hex number “64” represents the decimal number 100.

Given Data / Assumptions:

• Hexadecimal digits: 0–9, A(10), B(11), C(12), D(13), E(14), F(15).
• Number to convert: 0x64 (hex).
• Positional weights in base 16: 16^1 and 16^0 for the two digits.

Concept / Approach:To convert hex to decimal, multiply each digit by its positional weight and sum. For 0x64, the left digit is 6 and the right digit is 4. Therefore, value = 6*16 + 4*1. Compute and compare with 100 in decimal to verify the statement.

Step-by-Step Solution:

Verification / Alternative check:Use a mental cross-check: 0x64 is often remembered because 0x64 = 100, 0x32 = 50, and 0x0A = 10 in decimal. These are common anchor points for programmers.

Why Other Options Are Wrong:

• Incorrect: The arithmetic confirms the statement.
• “Correct only for base-8” / “ignore the trailing 4”: Both are irrelevant or nonsensical to proper base-16 conversion.

Common Pitfalls:Misinterpreting “64” as decimal 64 instead of hex 0x64; forgetting place values differ by powers of 16 in hexadecimal.

Final Answer:Correct — 0x64 equals 100 in decimal.