Convert the binary number 101101 (base 2) to its decimal (base 10) value. Show the place-value reasoning clearly.

Introduction / Context:
Binary-to-decimal conversion illustrates how positional number systems work. Each bit represents a power of two based on its position from the rightmost bit (least significant bit). Converting 101101 (base 2) to decimal by explicit expansion builds confidence for handling larger values and for reading register contents and addresses.

Given Data / Assumptions:

• Binary string: 101101.
• Bit positions from right to left: 2^0, 2^1, 2^2, 2^3, 2^4, 2^5.
• Only positions with bit 1 contribute to the sum.

Concept / Approach:
Write the value as a sum of weighted bits: value = Σ(bit_i * 2^i). For 101101, the 1s occur at positions 0, 2, 3, and 5 (counting from 0 on the right). Compute each contributing power and add them to obtain the decimal result.

Step-by-Step Solution:
List powers of two: 2^0=1, 2^1=2, 2^2=4, 2^3=8, 2^4=16, 2^5=32.Map bits: 1 0 1 1 0 1 → positions 5, 3, 2, 0 are 1.Compute sum: 2^5 + 2^3 + 2^2 + 2^0 = 32 + 8 + 4 + 1 = 45.Decimal result: 45.

Verification / Alternative check:
Group into two parts: 101000 (binary) = 40 and 000101 (binary) = 5; 40 + 5 = 45, confirming the same answer with a quick mental split.

Why Other Options Are Wrong:
43 misses one 2^1 contribution or miscounts a bit; 40 corresponds to 101000; 47 would require an extra 2^1 compared to our number; “None” is wrong because 45 is correct.

Common Pitfalls:
Reading positions from the left instead of the right; dropping a middle bit; arithmetic slips when adding powers quickly. Always enumerate the powers and mark the 1-bit positions.

Final Answer:
45