Binary to decimal conversion in digital electronics: What is the decimal (base 10) value of the binary number 1100011₂?

Introduction / Context:
Converting binary numbers to decimal is a foundational skill in digital electronics and computer engineering. The question asks for the base-10 value of the binary number 1100011₂. Understanding place values for powers of 2 ensures accurate and quick conversions needed for debugging, data interpretation, and low-level programming.

Given Data / Assumptions:

• Binary input: 1100011₂.
• Target: decimal (base 10) representation.
• No leading zeros to consider; the bit-width remains 7 bits as written.

Concept / Approach:
Each bit in a binary number represents a power of 2, starting from the rightmost bit as 2^0, then 2^1, 2^2, and so on. To convert, multiply each bit by its corresponding power of 2 and sum the results. Only positions with bit value 1 contribute to the sum; positions with 0 contribute nothing.

Step-by-Step Solution:
Write positional weights for 7 bits: 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0 → 64, 32, 16, 8, 4, 2, 1.Map bits: 1 1 0 0 0 1 1 (from MSB to LSB).Multiply and add only 1-bits: 64 + 32 + 2 + 1.Compute sum: 64 + 32 = 96; 96 + 2 = 98; 98 + 1 = 99.Therefore, 1100011₂ = 99₁₀.

Verification / Alternative check:
Group into convenient chunks: (110)_2 = 6 and (0011)_2 = 3 does not directly apply because the bit groups are unequal; however, a calculator or quick mental addition of powers (64 + 32 + 2 + 1) reconfirms the answer 99₁₀.

Why Other Options Are Wrong:
97₁₀ or 93₁₀ omit one or more powers of 2 in the sum. 29₁₀ is far smaller than the MSB contribution (64) plus the next (32), so it cannot be correct for a 7-bit value starting with 11xxxxx.

Common Pitfalls:
Reading bits right-to-left incorrectly, forgetting a power (often 2^1 = 2), or adding a nonexistent 2^2 term. Always list the powers beneath the bits before summing.

Final Answer:
99₁₀