How do you convert hexadecimal to decimal?

Hex to decimal: multiply each digit by its positional power of 16 and sum the results. Positions are counted from right starting at 0. Formula: decimal = sum of (hex digit value × 16^position) Hex digit values: 0-9 are their face value; A=10, B=11, C=12, D=13, E=14, F=15. Examples: - FF: (15×16^1) + (15×16^0) = 240 + 15 = 255 - 1A: (1×16^1) + (10×16^0) = 16 + 10 = 26 - DEAD: (13×16^3) + (14×16^2) + (10×16^1) + (13×16^0) = 53248 + 3584 + 160 + 13 = 57005

How do you convert decimal to hexadecimal?

Decimal to hex: repeatedly divide by 16 and collect remainders. Remainders 10-15 become A-F. Read bottom to top. Example: convert 255 to hex 255 ÷ 16 = 15 remainder 15 → F 15 ÷ 16 = 0 remainder 15 → F Read bottom to top: FF Example: convert 26 to hex 26 ÷ 16 = 1 remainder 10 → A 1 ÷ 16 = 0 remainder 1 → 1 Read bottom to top: 1A Verification: 1×16 + 10 = 26 ✓ Quick reference: - 0-9 → 0-9 - 10 → A - 15 → F - 16 → 10 - 255 → FF - 256 → 100

What is the relationship between hex and binary?

Hex and binary have a perfect relationship: each hex digit represents exactly 4 binary bits (a nibble). This makes conversion trivial — no arithmetic needed. Hex to binary: replace each hex digit with its 4-bit binary equivalent. - F = 1111 - A = 1010 - FA = 1111 1010 - FF = 1111 1111 Binary to hex: group bits in 4 from the right, convert each group. - 1010 1111 → A F → AF - 0001 1010 → 1 A → 1A This is why programmers use hex: it is a compact representation of binary. One byte (8 bits) needs exactly 2 hex digits. A 32-bit value needs exactly 8 hex digits. A 64-bit value needs 16 hex digits.

Where is hexadecimal used in programming and computing?

Hexadecimal appears throughout computing: Colour codes: #FF5733 = R:255 G:87 B:51. Web colours, CSS, and design tools all use 6-digit hex strings where each pair is one colour channel. Memory addresses: 0x7FFE1234. Debuggers, assembly language, and memory maps use hex because it maps directly to binary. ASCII and Unicode: 'A' = 0x41, space = 0x20, newline = 0x0A. Character encoding tables use hex. MAC addresses: 00:1A:2B:3C:4D:5E — six hex pairs separated by colons. File formats: hex editors show raw file bytes as hex pairs. Magic bytes (file signatures) like FF D8 FF (JPEG) and 89 50 4E 47 (PNG) identify file types. IP addresses and network: subnet masks, IPv6 addresses (2001:0db8:85a3::8a2e:0370:7334). Flags and bitmasks: 0xFF, 0x0F, 0xF0 are clean hex masks for bit manipulation.

What does 0x mean before a hexadecimal number?

0x is the standard prefix for hexadecimal numbers in most programming languages. It tells the compiler or interpreter that the following digits are in base 16. Examples: - 0xFF = 255 in decimal - 0x1A = 26 - 0xDEAD = 57005 - 0x100 = 256 Origin: the 0 prevents the number from being read as a variable name, and x stands for hexadecimal. Other prefixes by language and base: - 0b = binary (Python, JavaScript): 0b1010 = 10 - 0o = octal (Python): 0o77 = 63 - 0 = octal (C/C++): 077 = 63 (legacy, confusing) - # = hex (CSS colours, assembly): #FF or $FF - H suffix (assembly): FFH This calculator accepts numbers with or without the 0x prefix — it strips it automatically.

Hexadecimal Converter — Hex to Decimal, Binary, Octal

The Hexadecimal Converter converts hex numbers to decimal, binary, and octal instantly. Enter any hex value (0-9, A-F) and all four base representations appear simultaneously with one-click copy. Step-by-step working shows the positional expansion for hex-to-decimal and repeated division for decimal...

HEX CONVERTER

CONVERT FROM

Enter Hexadecimal number(0-9, A-F)

Hexadecimal (base 16)

input

Decimal (base 10)

255

Binary (base 2)

11111111

Octal (base 8)

377

Bit length

Bytes

0x prefix

0xFF

STEP-BY-STEP

Hex: FF

Expand: F×16^1 = 240 + F×16^0 = 15

= 255 (decimal)

Decimal 255 ÷ 2 repeatedly → binary: 11111111

Binary nibbles: 1111 1111 → Hex: FF

QUICK EXAMPLES

BIT PATTERN

Byte 1

HEX DIGIT TABLE

A10

B11

C12

D13

E14

F15

Created with❤️byeaglecalculator.com

HOW TO USE

1
The converter defaults to Hexadecimal input. Type your hex number using digits 0-9 and letters A-F (case insensitive). The 0x prefix is optional and stripped automatically.
2
Switch the input base using the four buttons if you want to convert from decimal, binary, or octal instead. All four conversions always show simultaneously.
3
The step-by-step panel shows the positional expansion for hex input (each digit × its power of 16) and the repeated division method for decimal-to-hex conversion.
4
The hex digit reference table on the right shows all 16 hex digits (0-F) with their decimal equivalents. The bit pattern visualiser shows the binary representation in coloured bit cells.
5
Click any Copy button next to a result to copy that value to clipboard. Use the quick example buttons to try common values: FF (255), 1A (26), DEAD (57005), FFFF (65535).

WORKED EXAMPLE

FF hex: F×16^1 + F×16^0 = 240+15 = 255 decimal = 11111111 binary = 377 octal. 1A hex: 1×16+10 = 26 decimal = 11010 binary = 32 octal. Decimal 255 to hex: 255÷16=15 r15(F), 15÷16=0 r15(F) → FF. Bit pattern FF = 11111111 (8 bits all on). DEAD hex = 57005 decimal.

FORMULAS

HEX CONVERSION REFERENCE

NAME	FORMULA	DESCRIPTION
Hex to decimal	Sum of (digit × 16^position)	FF = 15×16 + 15×1 = 255
Decimal to hex	Repeated division by 16, read remainders bottom-up	255 ÷ 16 = 15 r 15(F), 15 ÷ 16 = 0 r 15(F) → FF
Hex to binary	Replace each hex digit with its 4-bit binary	FF → 1111 1111
Binary to hex	Group bits in 4 from right, convert each	1010 1111 → A F → AF
Hex digit values	A=10, B=11, C=12, D=13, E=14, F=15	Letters extend digits beyond 9
1 byte in hex	2 hex digits = 8 bits = 0x00 to 0xFF	Max byte value: FF = 255
0x prefix	0xFF = 255 (hex prefix convention)	Used in code: 0x1A, 0xFF, 0xDEAD
Nibble	1 hex digit = 4 bits = 1 nibble	Half a byte

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Last updated: April 29, 2026 · Formula verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.