Binary-to-decimal conversion practice Convert the binary number 10011010 (base 2) to its decimal (base 10) equivalent.

Introduction / Context:Binary-to-decimal conversion is a fundamental skill in digital electronics and computer science. Each binary digit (bit) represents a power of 2, and the decimal value is the sum of those powers where bits are 1.

Given Data / Assumptions:

• Binary input: 10011010₂.
• We seek the decimal (base 10) value.
• No leading zeros change the magnitude.

Concept / Approach:For a binary string b7 b6 b5 b4 b3 b2 b1 b0, the decimal value is sum(bi * 2^i) for i from 0 to 7. Only positions with bi = 1 contribute to the sum.

Step-by-Step Solution:

Verification / Alternative check:Group into nibbles: 1001 1010 → 0x9A in hex. Hex 0x9A = 9*16 + 10 = 144 + 10 = 154, confirming the result.

Why Other Options Are Wrong:

• 153, 155, 157: off by small amounts, typically from misreading one bit's place value (16, 8, or 2).

Common Pitfalls:Forgetting that the leftmost bit is the highest power of 2, or mixing up 2^3=8 and 2^4=16.

Final Answer:154