Tool Number Base Converter
Pick the base you're entering from, type your number, and instantly see it converted to Binary (base 2), Octal (base 8), Decimal (base 10), and Hexadecimal (base 16). An interactive bit diagram illustrates individual binary bits at a glance.
Enter a decimal number (digits 0–9). You can include a negative sign for signed numbers.
Explained How Base Conversion Works
Every number can be represented across multiple mathematical bases. The base (or radix) determines the number of unique symbols used and what positional value each digit represents.
The Four Common Bases
| Base | Name | Digits Used | Example | Decimal Value |
|---|---|---|---|---|
| 2 | Binary | 0, 1 | 1010 | 10 |
| 8 | Octal | 0–7 | 12 | 10 |
| 10 | Decimal | 0–9 | 10 | 10 |
| 16 | Hexadecimal | 0–9, A–F | A | 10 |
Hex ↔ Decimal Reference
Hexadecimal uses letters A–F to represent the single-digit quantities from 10 to 15:
| Hex | Decimal | Binary |
|---|---|---|
| 0 | 0 | 0000 |
| 1 | 1 | 0001 |
| 2 | 2 | 0010 |
| 3 | 3 | 0011 |
| 4 | 4 | 0100 |
| 5 | 5 | 0101 |
| 6 | 6 | 0110 |
| 7 | 7 | 0111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| A | 10 | 1010 |
| B | 11 | 1011 |
| C | 12 | 1100 |
| D | 13 | 1101 |
| E | 14 | 1110 |
| F | 15 | 1111 |
Reading the Bit Diagram
In our bit diagram, each bit position carries a positional weight calculated as 2n (counting from 0 on the far right). To get the decimal value, simply sum the weights of all active (highlighted) bits.
1011 has bits at index 3, 1, and 0 set to 1. Total value = 2³ + 2¹ + 2⁰ = 8 + 2 + 1 = 11.Reference Common Conversions at a Glance
Frequently referenced benchmark values in computing, networking, and digital logic.
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 5 | 101 | 5 | 5 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 16 | 10000 | 20 | 10 |
| 32 | 100000 | 40 | 20 |
| 64 | 1000000 | 100 | 40 |
| 100 | 1100100 | 144 | 64 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
| 1024 | 10000000000 | 2000 | 400 |
FAQ Frequently Asked Questions
How do you convert binary to decimal?
Multiply each binary digit by 2 raised to its position (starting from 0 on the right) and sum the results. For example, 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11.
How do you convert decimal to binary?
Repeatedly divide the number by 2 and record the remainders. Then read the remainders from bottom to top. For example, 13 → 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 → binary 1101.
What is F in hexadecimal?
F in hexadecimal equals 15 in decimal and 1111 in binary. Hexadecimal uses digits 0–9 and letters A–F to cover values 0–15 in a single character.
How do you convert binary to hex quickly?
Group the binary digits into nibbles (sets of 4 bits) starting from the right, pad with leading zeros if needed, then convert each 4-bit chunk. For example, 1011 0010 = B2 in hex.
What's the difference between binary, hex, and decimal?
They represent the exact same numeric quantities in different radices. Binary uses base 2 (digits 0–1), decimal uses base 10 (digits 0–9), hex uses base 16 (digits 0–9 and A–F), and octal uses base 8 (digits 0–7).
Can I convert negative numbers?
Yes. Simply prefix your number with a minus sign (-). The tool will preserve the negative sign and convert the absolute magnitude across all target bases.
What does the visual bit diagram show?
Each box represents one bit. Green/teal highlighted boxes are bits that are 1 (on), while gray boxes are bits that are 0 (off). Below each bit is its power of 2 and its numerical weight.