Add the two binary numbers 110101 (base 2) and 101111 (base 2). Provide the final binary sum.

Introduction / Context:
Binary addition underlies arithmetic logic units (ALUs) and software integer arithmetic. Practicing manual addition clarifies carry propagation and helps validate results when debugging or designing datapaths. We add 110101₂ and 101111₂ and express the result in binary.

Given Data / Assumptions:

• Augend: 110101 (base 2).
• Addend: 101111 (base 2).
• Standard binary addition rules apply: 0+0=0, 0+1=1, 1+1=0 with carry 1, 1+1+carry=1 with carry 1, etc.

Concept / Approach:
Perform column-wise addition from least significant bit to most significant bit, tracking carries. Alternatively, convert to decimal, add, and reconvert to binary for a quick check. 110101₂ = 53₁₀ and 101111₂ = 47₁₀, so the sum should be 100₁₀, which hints that the binary result should be 1100100₂ (64+32+4).

Step-by-Step Solution:
Write the numbers aligned: 110101 + 101111.LSB column: 1+1=0 carry 1.Next: 0+1+carry1=0 carry 1.Next: 1+1+carry1=1 carry 1.Next: 0+1+carry1=0 carry 1.Next: 1+0+carry1=0 carry 1.MSB: 1+1(carry)=10 → write 10 at the left, final result 1100100.

Verification / Alternative check:
Decimal check: 53 + 47 = 100. Convert 1100100₂: 64 + 32 + 4 = 100. Both methods agree.

Why Other Options Are Wrong:
1101000 equals 104; 1110111 equals 119; 110011 equals 51; “None” is wrong because 1100100 is correct.

Common Pitfalls:
Losing a carry in the middle columns; forgetting that 1+1=0 carry 1; misaligning bits. Always track carries systematically and verify with a decimal cross-check if time permits.

Final Answer:
1100100