How-to guides · 3 min read
Binary to Decimal Conversion: A Clear Step-by-Step Method
Place values in binary
From the right the places are 1, 2, 4, 8, 16, 32 … (powers of 2). Add the places that have a 1.
1101 (binary) → decimal
- 1101 (base 2) = 13 (base 10)
- Decimal: 13
Step-by-step working 1 steps
- 1Convert from base 2 to decimal
1 × 2^3 = 8 1 × 2^2 = 4 0 × 2^1 = 0 1 × 2^0 = 1 Sum = 13
Each digit is multiplied by its place value, a power of the base.
Decimal to binary
Divide by 2 repeatedly and record the remainders; read them from the bottom up.
45 (decimal) → binary
- 45 (base 10) = 101101 (base 2)
- Decimal: 45
Step-by-step working 2 steps
- 1Already decimal
45
- 2Convert decimal to base 2 by repeated division
45 ÷ 2 = 22 remainder 1 22 ÷ 2 = 11 remainder 0 11 ÷ 2 = 5 remainder 1 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1
Read the remainders from bottom to top.
Hexadecimal shortcut
Group bits in fours: 1111 1111 is FF, which is 255. Colour codes like #FF8800 are three bytes in hex. Try the base converter.
Why it matters
Computers store everything as bits, and sizes grow as powers of 2. Understanding place value is the same skill used in base ten.
Frequently asked questions
What is 10 in binary?
1010.
How many values can 8 bits hold?
2⁸ = 256, from 0 to 255.
Keep reading
Roman Numerals Chart 1 to 100 With Conversion Rules
Every Roman numeral from 1 to 100 in a printable chart, with the seven symbols, the subtractive rule and how to read or write any numeral.
Charts & referencesPowers of 2 Table: 2⁰ to 2²⁰ and Why Computers Love Them
Powers of two from 2⁰ to 2²⁰ plus 2³², with binary, byte and memory examples, and how doubling grows faster than most people expect.
How-to guidesHow to Convert a Decimal to a Fraction (Including Repeating)
Turn terminating and repeating decimals into simplified fractions with step-by-step examples: 0.375, 0.6 and 0.333…
How-to guidesHow to Round Numbers: Decimal Places and Significant Figures
The rules for rounding to decimal places, significant figures and the nearest ten, hundred or other multiple, with edge cases like 1.005.