Convert the binary number 110001 (base 2) to its decimal (base 10) value. Show the place-value reasoning clearly.

Introduction / Context:
Converting from binary (base 2) to decimal (base 10) reinforces understanding of positional number systems. Each bit represents a power of 2 based on its position from the rightmost bit (least significant bit). We will convert 110001 (base 2) to decimal using place-value expansion.

Given Data / Assumptions:

• Binary digits are 1 1 0 0 0 1 from left to right.
• Positions from rightmost: 2^0, 2^1, 2^2, 2^3, 2^4, 2^5.
• Only positions with bit 1 contribute to the sum.

Concept / Approach:
Interpret the binary as a weighted sum: value = sum(bit_i * 2^i). For 110001, bits set to 1 are at positions 5, 4, and 0 (counting from 0 on the right). Therefore, decimal value = 2^5 + 2^4 + 2^0 = 32 + 16 + 1.

Step-by-Step Solution:
Write powers of two: 2^0=1, 2^1=2, 2^2=4, 2^3=8, 2^4=16, 2^5=32.Map bits: 1 1 0 0 0 1 corresponds to 2^5 + 2^4 + 02^3 + 02^2 + 0*2^1 + 2^0.Compute the sum: 32 + 16 + 1 = 49.State the decimal value: 49.

Verification / Alternative check:
Group as 110000 + 000001 (base 2). 110000 (base 2) = 48, and 000001 (base 2) = 1. Sum = 49. Both methods agree.

Why Other Options Are Wrong:
27: would correspond to 11011 (base 2), not 110001.39: corresponds to 100111 (base 2), not 110001.50: would be 110010 (base 2), one more than our number.None of the above: incorrect because 49 is exactly correct.

Common Pitfalls:
Misaligning bit positions; forgetting that any 0 bit contributes nothing; reading from left instead of right when assigning powers; arithmetic slips when adding powers of two quickly.

Final Answer:
49