What is a nibble, byte, and word in computing?

A nibble is 4 bits (one hex digit, values 0–15). A byte is 8 bits (two hex digits, values 0–255). A word is typically 16, 32, or 64 bits depending on the CPU architecture. A 32-bit word can hold values 0–4,294,967,295 (0 to 0xFFFFFFFF in hex).

Everyday Utility

Number Base Converter

Convert numbers between decimal, binary, hexadecimal, and octal instantly.

Select input base, then type your number

Enter Decimal number

Valid characters: 0123456789

Number Properties (decimal 255)

Decimal

255

Bits needed

Bytes needed

Is even?

Common Values Reference Table

Decimal	Binary	Octal	Hex
0	0000	0	0
1	0001	1	1
2	0010	2	2
4	0100	4	4
7	0111	7	7
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	0001 0000	20	10
32	0010 0000	40	20
64	0100 0000	100	40
128	1000 0000	200	80
255	1111 1111	377	FF
256	0001 0000 0000	400	100
512	0010 0000 0000	1000	200
1024	0100 0000 0000	2000	400

Understanding Number Bases

A number base (or radix) defines how many unique digits a number system uses. The decimal system (base 10) that we use daily has digits 0–9. Binary (base 2) has only 0 and 1. Octal (base 8) uses 0–7. Hexadecimal (base 16) uses 0–9 plus A–F to represent values 10–15.

These number systems aren't just academic — they're the foundation of modern computing. Every piece of data a computer stores or processes is ultimately binary. Hexadecimal provides a human-readable shorthand for binary: since 16 = 2⁴, each hex digit perfectly represents exactly 4 binary bits, making it far more compact than writing out long strings of 0s and 1s.

Understanding base conversion is useful for web developers (CSS color codes), security professionals (reading hex-encoded data), computer science students, and anyone working with low-level systems or networking.

The Four Common Bases

Binary (Base 2)

Digits: 0, 1

Used for: Computer hardware, logic gates, bitwise operations, networking masks

255 = 1111 1111

Octal (Base 8)

Digits: 0–7

Used for: Unix/Linux file permissions (chmod), legacy systems

255 = 377

Decimal (Base 10)

Digits: 0–9

Used for: Human everyday math, currency, most user-facing displays

255 = 255

Hexadecimal (Base 16)

Digits: 0–9, A–F

Used for: Memory addresses, color codes, cryptographic hashes, bytecode

255 = FF

Conversion Methods

Decimal → Binary (Repeated Division by 2)

Convert 42 to binary:

42 ÷ 2 = 21 R0

21 ÷ 2 = 10 R1

10 ÷ 2 = 5 R0

5 ÷ 2 = 2 R1

2 ÷ 2 = 1 R0

1 ÷ 2 = 0 R1

Read remainders bottom-up → 101010

Binary → Decimal (Positional Value)

Convert 1010 1100 to decimal:

1×2⁷ + 0×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 0×2⁰

= 128 + 0 + 32 + 0 + 8 + 4 + 0 + 0 = 172

Hex → Binary (Group of 4 bits)

Each hex digit = exactly 4 binary bits:

A = 1010, B = 1011, C = 1100, D = 1101

E = 1110, F = 1111, 5 = 0101, 7 = 0111

So: 0x5F = 0101 1111 = decimal 95

And: 0xFF = 1111 1111 = decimal 255

Real-World Uses of Number Bases

Web Colors (CSS)

#FF6600 is hex for RGB(255, 102, 0). FF=255 red, 66=102 green, 00=0 blue. Hex is compact and human-readable for 24-bit color values.

IPv4 Networking

Subnet masks like 255.255.255.0 are expressed as decimals but are really binary masks. 255 = 1111 1111 — all 8 bits set.

Unix Permissions

chmod 755 = 111 101 101 in binary. Owner: rwx (7), Group: r-x (5), Other: r-x (5). Octal is a natural fit for 3-bit permission groups.

Memory Addresses

RAM addresses are shown in hex: 0x00400000. A 64-bit address space goes from 0x0 to 0xFFFFFFFFFFFFFFFF.

ASCII / Unicode

The letter 'A' is 0x41 (hex) = 65 (decimal) = 0100 0001 (binary). Character encoding tables always use hex for readability.

Cryptographic Hashes

SHA-256 hashes are 256-bit binary outputs displayed as 64 hex characters. e.g. a3f8...d2c1 is 256 bits in 64 hex digits.

Frequently Asked Questions

How do I convert binary to decimal?

Multiply each bit by 2 raised to its position (right to left, starting at 0) and sum. For 1011: 8+0+2+1 = 11.

How do I convert decimal to binary?

Repeatedly divide by 2, record remainders, read bottom-up. 13 → R1, R0, R1, R1 → 1101.

What is hexadecimal and why is it used?

Base 16, using 0–9 and A–F. Each hex digit = 4 binary bits. Used for memory addresses, color codes, and bytecode because it compactly represents binary data.

How do I convert hexadecimal to decimal?

Multiply each digit by 16 raised to its position. For 2F: (2×16) + (15×1) = 32+15 = 47. A=10, B=11, C=12, D=13, E=14, F=15.

What is octal (base 8)?

Digits 0–7. Each octal digit = 3 binary bits. Used in Unix file permissions (chmod 755). Decimal 8 = octal 10.

What does 0x mean before a number?

The 0x prefix indicates hexadecimal in programming. 0xFF = 255 decimal. 0b prefix = binary; 0o prefix = octal.

How many binary digits does a decimal number need?

Bits = floor(log₂(n)) + 1. So 255 needs 8 bits. A byte (8 bits) holds 0–255.

What is a nibble, byte, and word?

Nibble = 4 bits (one hex digit, 0–15). Byte = 8 bits (two hex digits, 0–255). Word = 16/32/64 bits depending on CPU architecture.

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Methodology & Disclaimer

Calculation method: Converts via JavaScript's parseInt(value, fromBase) and Number.toString(toBase). Supports non-negative integers. Input is validated to only accept characters valid for the selected base. Hex output is uppercase. Binary output is grouped in nibbles (4 bits) for readability. Last updated: September 2026. Maintained by The Free Calculator Site.