Binary to decimal — 8-bit example Evaluate the decimal value of the binary number 11001110₂.
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
-
A12
-
B206
-
C127
-
D66
Answer
Correct Answer: 206
Explanation
Introduction / Context:Converting an 8-bit binary pattern to decimal requires summing the place values (powers of two) where the bits are 1. This is foundational for interpreting register dumps, opcodes, and pixel values.
Given Data / Assumptions:
- Binary input: 11001110.
- Bit positions correspond to 2^7 down to 2^0.
- No sign-bit interpretation (treat as unsigned).
Concept / Approach:For b7 b6 b5 b4 b3 b2 b1 b0 = 11001110, compute sum(bi * 2^i). Only positions with bi = 1 contribute to the sum: 2^7, 2^6, 2^3, 2^2, 2^1.
Step-by-Step Solution:
1) 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) Bits set: b7=1 (128), b6=1 (64), b5=0, b4=0, b3=1 (8), b2=1 (4), b1=1 (2), b0=0.3) Sum: 128 + 64 + 8 + 4 + 2 = 206.4) Therefore, 11001110₂ = 206₁₀.Verification / Alternative check:Group into nibbles: 1100 1110 → 0xCE. Hex CE equals 12*16 + 14 = 192 + 14 = 206, confirming the result.
Why Other Options Are Wrong:
- 12: off by an order of magnitude.
- 127: maximum for 7 bits set; does not match this pattern.
- 66: equals 64 + 2 only; ignores other set bits.
Common Pitfalls:Miscounting powers of two or forgetting to include the 8 and 4 positions in the sum.
Final Answer:206