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

Difficulty: Easy

Correct Answer: 154

Explanation:


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:

1) Write place values: 2^7=128, 2^6=64, 2^5=32, 2^4=16, 2^3=8, 2^2=4, 2^1=2, 2^0=1.2) Map bits (10011010): 1·128 + 0·64 + 0·32 + 1·16 + 1·8 + 0·4 + 1·2 + 0·1.3) Sum contributions: 128 + 16 + 8 + 2 = 154.4) Therefore, decimal value = 154.


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

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