# Binary to Hexadecimal Calculator

Convert between binary and hexadecimal instantly. Also shows decimal and octal. Includes 4-bit grouping and bit count for programming and digital electronics.

## What this calculates

Convert between binary and hexadecimal number systems. Enter a number and see it represented in binary (base 2), hexadecimal (base 16), decimal (base 10), and octal (base 8). The binary output is grouped in 4-bit nibbles for easy reading.

## Inputs

- **Decimal Equivalent** — min 0, max 2147483647 — Enter the number in decimal. The calculator shows binary, hex, and other bases.

## Outputs

- **Binary (Base 2)** — formatted as text — The number in binary.
- **Binary (4-bit groups)** — formatted as text — Binary with nibble spacing for readability.
- **Hexadecimal (Base 16)** — formatted as text — The number in hexadecimal.
- **Hex (0x prefix)** — formatted as text — Hexadecimal with the 0x programming prefix.
- **Decimal (Base 10)** — formatted as text — The number in decimal.
- **Octal (Base 8)** — formatted as text — The number in octal.
- **Bits Required** — Minimum number of bits to represent this value.

## Details

Binary and hexadecimal have a natural relationship: each hexadecimal digit maps to exactly 4 binary digits (bits). This makes converting between them quick once you know the mapping.

**Binary to Hex Nibble Table:**

| Binary | Hex | Decimal |
|--------|-----|--------|
| 0000 | 0 | 0 |
| 0001 | 1 | 1 |
| 0010 | 2 | 2 |
| 0011 | 3 | 3 |
| 0100 | 4 | 4 |
| 0101 | 5 | 5 |
| 0110 | 6 | 6 |
| 0111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1001 | 9 | 9 |
| 1010 | A | 10 |
| 1011 | B | 11 |
| 1100 | C | 12 |
| 1101 | D | 13 |
| 1110 | E | 14 |
| 1111 | F | 15 |

**How to convert manually:** Group the binary digits into sets of 4 from the right (pad with leading zeros if needed). Then replace each group with its hex digit. Example: 11010110 becomes 1101 0110, which is D6.

**Why this matters:** Network engineers read MAC addresses in hex. Embedded developers read register values in hex. Security analysts examine binary file headers in hex. Understanding this conversion is fundamental in computing.

## Frequently Asked Questions

**Q: How do I convert binary to hexadecimal?**

A: Group the binary number into sets of 4 digits from right to left, padding with zeros on the left if needed. Then convert each 4-digit group to its hex equivalent (0000=0, 0001=1, ..., 1010=A, ..., 1111=F). Example: 10110011 groups as 1011 0011, which converts to B3.

**Q: Why does each hex digit equal exactly 4 bits?**

A: Hexadecimal is base 16, and 16 = 2^4. So 4 binary digits can represent values 0-15, which is exactly the range of a single hex digit (0-F). This perfect power-of-two relationship is why hex is the preferred shorthand for binary data.

**Q: What is a nibble?**

A: A nibble (or nybble) is a 4-bit unit, which is half a byte. One nibble corresponds to one hexadecimal digit. A byte (8 bits) is two nibbles, which is why a byte is always exactly two hex digits (00 to FF).

**Q: How do I convert hexadecimal to binary?**

A: Replace each hex digit with its 4-bit binary equivalent. For example, hex A3 becomes 1010 0011: A = 1010 and 3 = 0011. Concatenate the groups and drop any unnecessary leading zeros.

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Source: https://vastcalc.com/calculators/conversion/binary-to-hexadecimal
Category: Conversion
Last updated: 2026-04-08