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Number Base Explainer - Online Learn Binary, Hex

Educational Math binary explainer hex number base
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Number Base Explainer

Visualize & understand binary, octal, decimal, and hexadecimal conversions instantly

Number
Binary Base 2
101010
0-1 digits
Octal Base 8
52
0-7 digits
Decimal Base 10
42
0-9 digits
Hexadecimal Base 16
2A
0-9, A-F
Place Value Breakdown
Base 2
1×32 + 0×16 + 1×8 + 0×4 + 1×2 + 0×1 = 42

Each digit is multiplied by the base raised to its position power, then summed.

Conversion Steps Decimal → Binary via division by 2
Quick Reference: Numbers 0–15
Decimal Binary Octal Hexadecimal
0000000
1000111
2001022
3001133
4010044
5010155
6011066
7011177
81000108
91001119
10101012A
11101113B
12110014C
13110115D
14111016E
15111117F
Why Binary?

Computers use binary because transistors have only two reliable states: ON (1) and OFF (0). All digital data is ultimately stored as bits.

Hex in the Wild

Hex is widely used for color codes (#FF5733), memory addresses, MAC addresses, and Unicode code points (U+1F600 = 😀).

Octal Legacy

Octal was popular on older systems with 6-bit bytes (PDP-8). Today it's still used in Unix file permissions (e.g., chmod 755).

Frequently Asked Questions

A number base (or radix) defines how many unique digits a numeral system uses before incrementing to the next place value. Base 10 (decimal) uses digits 0–9. Base 2 (binary) uses only 0 and 1. Base 16 (hexadecimal) uses 0–9 plus A–F (representing 10–15). The base determines the weight of each position: in base b, the positions represent powers of b (…b³, b², b¹, b⁰).

Use the division by 2 method: repeatedly divide the decimal number by 2, recording the remainder each time. When you reach 0, read the remainders from bottom to top. Example: 42 → 42÷2=21 r0, 21÷2=10 r1, 10÷2=5 r0, 5÷2=2 r1, 2÷2=1 r0, 1÷2=0 r1. Reading up: 101010.

Use positional notation: each binary digit (bit) is multiplied by 2 raised to its position (starting from 0 at the rightmost). For 101010: 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 32 + 0 + 8 + 0 + 2 + 0 = 42. Our Place Value Breakdown panel above demonstrates this visually.

Hexadecimal is more compact than binary while mapping perfectly to it. One hex digit represents exactly 4 bits (a nibble). This makes hex ideal for representing bytes (2 hex digits = 8 bits = 1 byte), memory addresses, color codes, and binary data dumps. It's far easier to read 7F than 01111111.

Group binary digits into chunks of 4 starting from the right. Each 4-bit group converts directly to one hex digit. Example: 1010 1010 → AA (since 1010=10=A). Going the other way, expand each hex digit into its 4-bit binary equivalent. Use our Quick Reference table above as a cheat sheet!

Binary (Base 2): All digital computing, logic gates, data storage.
Octal (Base 8): Unix/Linux file permissions (chmod), legacy systems.
Decimal (Base 10): Everyday human counting and arithmetic.
Hexadecimal (Base 16): Color codes, memory addresses, MAC addresses, Unicode, binary data representation.

Yes! Just as decimal uses negative powers of 10 after the decimal point (0.5 = 5×10⁻¹), binary uses negative powers of 2. For example, 0.101₂ = 1×2⁻¹ + 0×2⁻² + 1×2⁻³ = 0.5 + 0 + 0.125 = 0.625 in decimal. This tool currently focuses on integers, but fractional conversion follows the same positional principle.
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