Convert Decimal to Binary
1 Decimal (dec) = 1 Binary (bin). Use the free converter below to instantly convert any decimal value to binary, or view the full conversion table and formula.
1 dec = 1 bin
Decimal to Binary Conversion Table
| Decimal (dec) | Binary (bin) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 7 | 111 |
| 8 | 1000 |
| 10 | 1010 |
| 15 | 1111 |
| 16 | 10000 |
| 20 | 10100 |
| 32 | 100000 |
| 50 | 110010 |
| 64 | 1000000 |
| 100 | 1100100 |
| 127 | 1111111 |
| 128 | 10000000 |
| 200 | 11001000 |
| 255 | 11111111 |
| 256 | 100000000 |
| 512 | 1000000000 |
| 1000 | 1111101000 |
| 1024 | 10000000000 |
| 2048 | 100000000000 |
| 4096 | 1000000000000 |
| 65535 | 1111111111111111 |
How to Convert Decimal to Binary
To convert decimal to binary, repeatedly divide the number by 2 and note the remainders. Read the remainders from bottom to top. For example, 42 in decimal: 42÷2=21 R0, 21÷2=10 R1, 10÷2=5 R0, 5÷2=2 R1, 2÷2=1 R0, 1÷2=0 R1 → 101010 in binary.
Worked Example: Convert 7 dec to bin
Start with the value in decimal
7 dec
Apply the formula
Repeatedly divide by 2, read remainders bottom-to-top
Calculate the result
7 dec = 111 bin
Decimal to Binary Examples
0 dec is equal to 0 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 0 dec converts to 0 bin.
1 dec is equal to 1 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 1 dec converts to 1 bin.
2 dec is equal to 10 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 2 dec converts to 10 bin.
7 dec is equal to 111 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 7 dec converts to 111 bin.
8 dec is equal to 1000 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 8 dec converts to 1000 bin.
10 dec is equal to 1010 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 10 dec converts to 1010 bin.
15 dec is equal to 1111 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 15 dec converts to 1111 bin.
16 dec is equal to 10000 bin. Using the formula Repeatedly divide by 2, read remainders bottom-to-top, 16 dec converts to 10000 bin.
Converting Binary to Decimal
Need the reverse conversion? Use the table below for a quick reference converting binary back to decimal.
| Binary (bin) | Decimal (dec) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
Decimal to Binary FAQ
How do I convert decimal to binary?
Repeatedly divide the decimal number by 2 and record the remainders. Read the remainders from bottom to top to get the binary result. For example, 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → 1101.
What is 255 in binary?
255 in decimal equals 11111111 in binary — a full byte with all 8 bits set to 1.
Why do computers use binary?
Computers use binary because digital circuits have two states: on (1) and off (0). All data — numbers, text, images — is ultimately stored and processed as sequences of binary digits (bits).
Understanding Decimal and Binary
What is a Decimal (dec)?
The decimal (dec) is a specialized unit of number systems. It is commonly abbreviated as dec and relates to binary by a factor of 1.
What is a Binary (bin)?
The binary (bin) is a specialized unit of number systems. It is commonly abbreviated as bin and relates to decimal by a factor of 1.