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Binary to decimal practice
An unsigned binary number uses powers of two as place values. Start at the rightmost bit with 2⁰, then move left through 2¹, 2² and so on.
By ExamCat · Original study lesson · Published September 24, 2026
Understand the method
A one contributes its place value and a zero contributes nothing. Leading zeros do not change an unsigned value. Signed formats require a separate interpretation, so do not apply an unsigned conversion silently to a signed bit pattern.
Worked example, step by step
Convert the unsigned binary number 10110 to decimal.
- Label places from left to right: 16, 8, 4, 2, 1.
- Keep places whose bits are one: 16, 4 and 2.
- Add 16 + 4 + 2 = 22.
- Check by decomposing 22 into distinct powers of two: 16 + 4 + 2 recreates 10110.
A mistake to watch for
Binary digits are not decimal digits wearing a new label: 10110 does not mean ten thousand one hundred ten in base two. Also specify bit width when overflow or signed values are involved.
Try it yourself: three questions
Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.
1. Convert unsigned 1111 to decimal.
Show answer and explanation
8 + 4 + 2 + 1 = 15.
2. Write decimal 9 as four unsigned bits.
Show answer and explanation
1001, using 8 + 1.
3. What is the largest unsigned value in eight bits?
Show answer and explanation
255, from 2⁸ − 1. There are 256 distinct bit patterns, including zero.
Build your next practice session
Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.
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Further reading
OpenStax: data structures and algorithms provides textbook background. The worked scenario and practice questions on this page were written independently for ExamCat.
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