How do I convert hexadecimal to decimal?

Multiply each hex digit by its place value (powers of 16) and sum the results. For example, hex FF: F(15) x 16¹ + F(15) x 16⁰ = 240 + 15 = 255. For quick conversion, hex digits 0-9 equal their decimal values, and A-F equal 10-15.

How do I read binary numbers?

Each binary digit represents a power of 2, starting from the right. For example, binary 1101 = 1x8 + 1x4 + 0x2 + 1x1 = 13 in decimal. The rightmost bit is 2⁰ (1), the next is 2¹ (2), then 2² (4), and so on.

What are hex color codes?

Hex color codes use six hexadecimal digits to represent RGB colors: the first two digits are red, the middle two are green, and the last two are blue. Each pair ranges from 00 (0) to FF (255). For example, #FF0000 is pure red, #00FF00 is green, and #FFFFFF is white.

Hex to Decimal Converter: Binary & Octal Too

Free hex to decimal, binary, and octal converter. Convert between number bases instantly with conversion tables, step-by-step formulas, and a free calculator.

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Understanding Number Systems

Computers and humans think about numbers differently. We use the decimal system (base 10) with digits 0-9, but computers work in binary (base 2) with just 0 and 1. Hexadecimal (base 16) and octal (base 8) bridge the gap — they’re compact ways to represent binary data in a human-readable format.

System	Base	Digits	Common Use
Binary	2	0, 1	Computer logic, networking
Octal	8	0-7	Unix file permissions
Decimal	10	0-9	Everyday counting
Hexadecimal	16	0-9, A-F	Colors, memory addresses

Hex to Decimal Conversion

Each hex digit represents a power of 16. To convert 0xFF to decimal:

F = 15, F = 15
0xFF = (15 × 16¹) + (15 × 16⁰)
     = (15 × 16) + (15 × 1)
     = 240 + 15
     = 255

Hex Color Codes

Web developers use hex codes for colors. Each pair of hex digits represents red, green, and blue (0-255):

Color	Hex Code	RGB Decimal
White	`#FFFFFF`	255, 255, 255
Black	`#000000`	0, 0, 0
Red	`#FF0000`	255, 0, 0
Green	`#00FF00`	0, 255, 0
Blue	`#0000FF`	0, 0, 255
Yellow	`#FFFF00`	255, 255, 0

Binary to Decimal Conversion

Each binary digit (bit) represents a power of 2. To convert 11010 to decimal:

1×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 16 + 8 + 0 + 2 + 0
= 26

How Computers Use Binary

All data in a computer is ultimately binary — a sequence of 0s and 1s. Each 0 or 1 is a bit, and 8 bits make a byte. Understanding binary helps with:

Networking: IP addresses and subnet masks
File sizes: Why 1 KB is 1024 bytes (2¹⁰)
Permissions: Unix chmod values
Programming: Bitwise operations and flags

For file size conversions, see our byte converter.

Octal to Decimal Conversion

Octal uses powers of 8. To convert 377 (octal) to decimal:

3×8² + 7×8¹ + 7×8⁰
= 192 + 56 + 7
= 255

Unix File Permissions

Octal is used for Unix/Linux file permissions:

Octal	Binary	Permission
7	111	Read + Write + Execute
6	110	Read + Write
5	101	Read + Execute
4	100	Read only
0	000	No permission

chmod 755 means: owner gets rwx (7), group gets r-x (5), others get r-x (5).

Quick Reference Table

Decimal	Hex	Binary	Octal
0	0	0	0
1	1	1	1
8	8	1000	10
10	A	1010	12
15	F	1111	17
16	10	10000	20
32	20	100000	40
64	40	1000000	100
128	80	10000000	200
255	FF	11111111	377
256	100	100000000	400

Free Hex Decimal Binary Converter

Convert between decimal, hexadecimal, binary, and octal number systems.

Example

Convert 0xA3 (hex) to decimal:

A = 10, 3 = 3
0xA3 = (10 × 16) + (3 × 1)
     = 160 + 3
     = 163

Frequently Asked Questions

How do I convert hex to decimal?

Multiply each hex digit by its positional power of 16, then add the results. Hex digits A-F represent values 10-15. For example, hex 1A = (1 x 16) + (10 x 1) = 26 in decimal. For larger numbers, continue with higher powers: 16², 16³, and so on.

Why do programmers use hexadecimal?

Hexadecimal is a compact way to represent binary data. Each hex digit maps to exactly 4 binary digits (bits), making conversion simple. For example, 0xFF = 11111111 in binary. This makes hex ideal for memory addresses, color codes, and byte values, which would be very long in binary.

What is the difference between binary and decimal?

Decimal (base 10) uses digits 0-9 and is what humans use daily. Binary (base 2) uses only 0 and 1 and is how computers process data. Binary is less readable but directly represents electrical states (on/off) in computer circuits. Every decimal number has a binary equivalent.

For Mac users looking for a calculator with built-in base conversion, check our best calculator apps for Mac comparison.

Convert Number Bases in Notes Calculator

Notes Calculator converts between decimal, hexadecimal, binary, and octal using natural syntax:

# Number Base Conversions
255 in hex
255 in binary
255 in octal

// Hex to decimal
0xFF in decimal

// Binary to decimal
0b11010 in decimal

// Arithmetic across bases
0xFF + 1 in hex
0b1010 + 0b0101 in binary

// Web color values
red = 0xFF
green = 0x80
blue = 0x00

Use hex, binary, octal, and decimal keywords (or their short forms ₁₆, ₂, ₈, ₁₀) to convert freely between systems. You can even do arithmetic across bases — Notes Calculator handles the conversion automatically.