Short answer
Binary to decimal: add the place values of the 1 bits, so 101101 = 32 + 8 + 4 + 1 = 45. Decimal to binary: divide by 2 and read the remainders upward. Binary to hex: group bits in fours, so 11111111 = FF.
1. Chart for 0 to 15
| Dec | Binary | Hex | Dec | Binary | Hex |
|---|---|---|---|---|---|
| 0 | 0000 | 0 | 8 | 1000 | 8 |
| 1 | 0001 | 1 | 9 | 1001 | 9 |
| 2 | 0010 | 2 | 10 | 1010 | A |
| 3 | 0011 | 3 | 11 | 1011 | B |
| 4 | 0100 | 4 | 12 | 1100 | C |
| 5 | 0101 | 5 | 13 | 1101 | D |
| 6 | 0110 | 6 | 14 | 1110 | E |
| 7 | 0111 | 7 | 15 | 1111 | F |
2. Binary to decimal
Each position is a power of 2, from 1 on the right. 101101 = 32 + 8 + 4 + 1 = 45.
3. Decimal to binary
Divide by 2 and keep the remainders: 45 → 22 r1, 22 → 11 r0, 11 → 5 r1, 5 → 2 r1, 2 → 1 r0, 1 → 0 r1. Read upward: 101101.
4. Binary to hex
Group the bits in fours from the right and use the chart. 101101 becomes 0010 1101, which is 2D. Check: 2 × 16 + 13 = 45.
5. Common values
| Binary | Decimal | Hex |
|---|---|---|
| 10000000 | 128 | 80 |
| 11001000 | 200 | C8 |
| 11111111 | 255 | FF |
| 1111101000 | 1000 | 3E8 |
| 1111111111 | 1023 | 3FF |
| 1111111111111111 | 65,535 | FFFF |
For other bases use the Number Base Converter, and to compute with binary use the Binary Calculator.
6. Frequently asked questions
How do I convert binary to decimal?expand_more
Add the place values (1, 2, 4, 8 and so on from the right) of every bit that is 1.
How do I convert decimal to binary?expand_more
Divide by 2 repeatedly and read the remainders from the bottom up.
How do I convert binary to hex?expand_more
Group the bits in fours from the right and replace each group with its hex digit.
What is 11111111 in decimal?expand_more
255, which is FF in hex.
7. Sources
- menu_bookBinary number (Wikipedia)