Binary result of a decimal addition — compute and encode. Problem: 49 + 1 in decimal; choose the correct 8-bit binary representation of the sum.

Introduction / Context:
Translating arithmetic results between bases is common in programming and digital design. Here we add two decimal numbers and then represent the sum in 8-bit binary (most significant bit first).

Given Data / Assumptions:

• Compute 49 + 1 = 50 (decimal)
• Encode 50 as an 8-bit binary number

Concept / Approach:
First do the decimal addition; then convert the result to binary by finding the sum of powers of two that equal 50. Alternatively, use repeated division by 2 or recall common binary values in the 32–63 range.

Step-by-Step Solution:

Verification / Alternative check:
Convert 00110010 back to decimal: 32 + 16 + 2 = 50, confirming correctness.

Why Other Options Are Wrong:

• 01010101 (85), 00110101 (53), 00110001 (49), 00110000 (48): each encodes a different decimal value, not 50.

Common Pitfalls:

• Confusing ASCII codes for characters '1' or '2' with numeric binary values; here we want the numeric binary for 50.

Final Answer:
00110010