conversion
Decimal to Binary Converter
Convert decimal numbers to binary. See the repeated division method step-by-step with remainders reading bottom to top.
Click to show tips
Try an Example
Pick a scenario to see how the calculator works, then adjust the values
ASCII Letter A
Convert the ASCII code for uppercase A (65) across all bases.
Key values: Decimal 65 · Binary 1000001 · Hex 41
Byte Maximum
The largest value a single byte can hold (255).
Key values: Decimal 255 · Binary 11111111 · Hex FF
Hex Color Code
Convert a common hex color code (deep sky blue) to other bases.
Key values: Hex 00BFFF · Decimal 49151 · Binary nibbles
The Division Method
Repeatedly divide the decimal number by 2 and record the remainders. The binary result is the remainders read bottom to top:
Reading remainders bottom-to-top: .
The Subtraction Method
Find the largest power of 2 that fits, subtract it, and repeat. Each power used is a 1 bit; each skipped power is a 0:
- → bit at = 1
- → bit at = 1
- → bit at = 0
- → bit at = 0
- → bit at = 1
Result: — same answer, more intuitive for some learners.
How Many Bits Do You Need?
The number of bits required to represent a decimal number is:
| Decimal range | Bits needed | Common name |
|---|---|---|
| 0–1 | 1 | Bit |
| 0–15 | 4 | Nibble |
| 0–255 | 8 | Byte |
| 0–65,535 | 16 | Word (16-bit) |
| 0–4,294,967,295 | 32 | Double word |
Negative Numbers: Two's Complement
Computers represent negative integers using two's complement: invert all bits, then add 1. For 8-bit numbers:
Why two's complement? It lets the same addition circuit handle both positive and negative numbers. The hardware doesn't need separate logic for subtraction — it just adds the two's complement.
Frequently Asked Questions
How do you convert decimal to binary?
Use the repeated division method: divide the number by 2, record the remainder, replace the number with the quotient, and repeat until the quotient is 0. Read the remainders from bottom to top for the binary result.
Is there a faster way to convert decimal to binary?
Yes, the subtraction method: find the largest power of 2 that fits, subtract it (that bit is 1), and repeat with the remainder. Each skipped power of 2 is a 0 bit. This can be more intuitive than repeated division.
How many bits do I need to represent a decimal number?
The formula is bits. Common ranges: 0–15 needs 4 bits (nibble), 0–255 needs 8 bits (byte), 0–65,535 needs 16 bits (word), and 0–4,294,967,295 needs 32 bits.
How do computers represent negative numbers in binary?
Most modern computers use two's complement: invert all bits and add 1. For example, in 8-bit binary is computed as 00011001 → invert → 11100110 → add 1 → 11100111.
Why is two's complement used instead of sign-magnitude?
Two's complement lets the same addition circuit handle both positive and negative numbers. The hardware does not need separate logic for subtraction; it simply adds the two's complement of the number being subtracted.
Related conversion Variants
Explore more conversion options
Binary to Decimal
Binary to Decimal Converter
Hex to Decimal
Hex to Decimal Converter
Decimal to Hex
Decimal to Hexadecimal Converter
Binary to Hex
Binary to Hexadecimal Converter
Octal to Decimal
Octal to Decimal Converter
More Math Calculators
Explore the category