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Basic conversion: What is the correct pure binary representation of the decimal number 42?

Difficulty: Easy

01000010
52
2A
101010

Correct Answer: 101010

Explanation:

Introduction / Context:
Converting between decimal and binary is a core skill in digital electronics. This item asks for the pure binary form of the decimal number 42, avoiding confusion with hexadecimal, octal, or ASCII encodings that sometimes appear similar.

Given Data / Assumptions:

Decimal value: 42.
Target: binary (base 2), no parity or additional coding.
Do not confuse with hex or character encodings.

Concept / Approach:
Use decomposition into powers of 2 or repeated division by 2. 42 can be written as a sum of powers of 2: 32 + 8 + 2. Setting bits at those positions yields the binary representation. Reading from the highest relevant power downward forms the final bit string without unnecessary leading zeros.

Step-by-Step Solution:

Find largest power of 2 ≤ 42 → 32 (2^5) → set bit 2^5 = 1, remainder 10.Next power ≤ 10 → 8 (2^3) → set bit 2^3 = 1, remainder 2.Next power ≤ 2 → 2 (2^1) → set bit 2^1 = 1, remainder 0.Bits (from 2^5 to 2^0): 1 0 1 0 1 0 → 101010.

Verification / Alternative check:
Convert back: 1*32 + 0*16 + 1*8 + 0*4 + 1*2 + 0*1 = 32 + 8 + 2 = 42. The value matches the original decimal.

Why Other Options Are Wrong:

01000010: This is 66 in decimal (also the ASCII code for the character “B”).52: That is the octal representation of 42 (base 8), not binary.2A: That is hexadecimal for 42, not binary.

Common Pitfalls:
Confusing bases due to similar-looking strings; assuming leading zeros are required; forgetting to express the full set of bits from the highest set bit down to 2^0.

Basic conversion: What is the correct pure binary representation of the decimal number 42?

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