Binary Coding Practice: Match Decimal Values to Their 8-bit Binary Equivalents List I (Decimal) A. 45 B. 90 C. 180 D. 210 List II (8-bit Binary) 10110100 11010010 01011010 00101101 10101000

Introduction / Context:Digital systems frequently require quick translation between decimal and binary. This problem reinforces binary conversion for common values, ensuring confidence when reading registers, bitmaps, or instruction encodings.

Given Data / Assumptions:

• 8-bit unsigned representation (leading zeros permitted).
• Decimal values: 45, 90, 180, 210.
• Binary candidates supplied as 8-bit strings.

Concept / Approach:

Convert each decimal number to binary using successive division by 2 or by decomposing into powers of 2. Then match to the list of 8-bit patterns.

Step-by-Step Solution:

Verification / Alternative check:

Hex cross-check: 45 = 0x2D = 0010 1101; 90 = 0x5A = 0101 1010; 180 = 0xB4 = 1011 0100; 210 = 0xD2 = 1101 0010. Hex-to-binary mapping confirms the 8-bit strings.

Why Other Options Are Wrong:

Each incorrect option mis-assigns at least one decimal-to-binary mapping, which will break in arithmetic or bit-test verification.

Common Pitfalls:

Dropping leading zeros (acceptable visually but confusing in fixed-width contexts) or mixing nibble order when transcribing hex to binary.

Final Answer:

A-4, B-3, C-1, D-2