Decimal to Binary Converter | Convert Decimal to Binary Numbers
Free online decimal to binary converter. Convert decimal numbers to binary with step-by-step explanations. Includes conversion tables and examples.
Decimal to Binary Converter
Powers of 2 Reference Table
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
How to Convert Decimal to Binary
Division Method
- Divide the decimal number by 2
- Write down the remainder (0 or 1)
- Divide the quotient by 2
- Repeat until quotient becomes 0
- Read the remainders from bottom to top
Converting 255 to Binary
255 ÷ 2 = 127 remainder 1
127 ÷ 2 = 63 remainder 1
63 ÷ 2 = 31 remainder 1
31 ÷ 2 = 15 remainder 1
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Result: 11111111
Converting 128 to Binary
128 ÷ 2 = 64 remainder 0
64 ÷ 2 = 32 remainder 0
32 ÷ 2 = 16 remainder 0
16 ÷ 2 = 8 remainder 0
8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Result: 10000000
Alternative Method: Power Subtraction
Another way to convert is by subtracting the largest power of 2 that fits:
Example: Converting 44 to Binary
44 - 32 (2⁵) = 12 → 1
12 - 8 (2³) = 4 → 1
4 - 4 (2²) = 0 → 1
Powers used: 2⁵, 2³, 2²
Result: 00101100
Practice Problems
Convert: 15₁₀
Answer: 1111₂
Convert: 64₁₀
Answer: 1000000₂
Convert: 100₁₀
Answer: 1100100₂
Quick Tips
Common Patterns
- Powers of 2 have a single 1 bit
- 15 = 1111 (all bits set in 4 bits)
- 255 = 11111111 (all bits set in 8 bits)
- Even numbers end in 0
Helpful Reminders
- Each bit doubles in value
- 8 bits = 1 byte
- Leading zeros don't change value
- Binary numbers can get long quickly
Related Conversions
About this Calculator
Free online decimal to binary converter. Convert decimal numbers to binary with step-by-step explanations. Includes conversion tables and examples.
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