Reading about binary-to-decimal conversion is one thing; actually converting a handful of numbers yourself is what makes the place-value method stick, so here are several worked examples ranging from simple to slightly trickier.
A Quick Recap of the Method
Every binary digit represents a power of two based on its position, counting from the right: 1, 2, 4, 8, 16, 32, 64, 128, and so on. To convert binary to decimal, add up the place values everywhere there’s a 1 and ignore the positions with a 0.
Example 1: 00000101
Reading right to left, there’s a 1 in the 4s place and a 1 in the 1s place, with 0s everywhere else. Adding 4+1 gives 5.
Example 2: 00010000
Only one 1 appears, in the 16s place. The answer is simply 16.
Example 3: 01011010
1s appear in the 64s, 16s, 8s, and 2s places. Adding 64+16+8+2 gives 90.
Example 4: 11111111
Every position has a 1, so every place value gets added: 128+64+32+16+8+4+2+1, which totals 255 — the largest number a single byte can represent.
Example 5: 00100100
1s appear in the 32s and 4s places. Adding 32+4 gives 36.
Common Mistakes to Watch For
The most frequent error is misreading which end of the binary number is the “ones” place — place values start from the rightmost digit, not the leftmost, so reading a number backward silently produces a completely different, often much larger, incorrect answer. Miscounting digits when the binary number is long is the second most common mistake, which is why lining up each digit under its power of two on paper helps avoid slips.
Bonus: Decimal to Binary Practice
The reverse process — converting decimal to binary — uses the same place values in reverse: repeatedly find the largest power of two that fits into the remaining number, mark that position with a 1, subtract it, and continue with what’s left. Converting 100, for example: 64 fits (mark 1, remainder 36), 32 fits (mark 1, remainder 4), 16 and 8 don’t fit (mark 0 for both), 4 fits (mark 1, remainder 0), and 2 and 1 don’t fit (mark 0 for both) — giving 01100100.
Check Your Own Answers
Our binary translator can convert any binary number back to check your work, and our step-by-step guide on how to read binary covers the full method in more depth if any of these examples felt rushed.