What is hexadecimal and why is it base-16?

Hexadecimal is a base-16 number system that uses 16 unique symbols: digits 0-9 and letters A-F. It is base-16 because each digit position represents a power of 16, just as decimal uses powers of 10. The system was adopted in computing because 16 is a power of 2 (2^4), meaning each hex digit maps perfectly to a 4-bit binary nibble. This makes hex an efficient and human-readable way to represent binary data. A single byte (8 bits) is expressed as exactly two hex digits, ranging from 00 to FF (0 to 255 in decimal).

How do you convert hex to decimal step by step?

To convert hex to decimal, multiply each digit by 16 raised to the power of its position, counting from 0 on the right, then add all the products. For example, hex 1A equals 1 x 16^1 + 10 x 16^0 = 16 + 10 = 26 in decimal. For larger numbers like hex B2F: B(11) x 16^2 + 2 x 16^1 + F(15) x 16^0 = 11 x 256 + 2 x 16 + 15 = 2,816 + 32 + 15 = 2,863. Most programming languages support this conversion natively using functions like parseInt("1A", 16) in JavaScript.

How do you add hexadecimal numbers?

You can add hex numbers by converting both to decimal, performing the addition, and converting the result back to hex. Alternatively, add digit by digit in base 16 from right to left, carrying 1 whenever a column sum exceeds 15 (F). For example, hex A + hex 7 = 17 in decimal = 11 in hex, so you write 1 and carry 1. This column-by-column method is faster for larger numbers and mirrors the long addition process you learned for decimal arithmetic.

Why is hexadecimal used in programming and web development?

Hexadecimal is used because each hex digit represents exactly 4 binary bits, making it a compact and readable way to express binary data. In web development, CSS hex color codes like #FF5733 use six hex digits to define red, green, and blue channels. In systems programming, memory addresses, MAC addresses, error codes, and cryptographic hashes are all written in hex. According to the W3C, over 90% of web pages use hex color notation in their stylesheets, making it one of the most widely used number formats outside of decimal.

What is the difference between hex, binary, octal, and decimal?

These are four different positional number systems distinguished by their base (radix). Decimal is base-10 with digits 0-9 and is the standard for everyday counting. Binary is base-2 with digits 0-1 and is the native language of computer hardware. Octal is base-8 with digits 0-7, historically used in early Unix systems for file permissions (e.g., chmod 755). Hexadecimal is base-16 with digits 0-F and is the preferred human-readable format for binary data. Use our binary calculator to perform arithmetic in base-2.

Hex Calculator

Quick Answer

Hexadecimal is the base-16 number system used throughout computing per IEEE standards, using digits 0-9 and letters A-F, where A=10 and F=15; this calculator adds, subtracts, multiplies, and divides hex values and converts to decimal, binary, and octal.

Also searched as: hex, hex calculator

Hexadecimal Arithmetic

Hex Value A

Operation

Hex Value B

Result (Hex)

119

Result (Decimal)

281

Number Base Converter

Input Value

Input Base

Decimal

255

Hexadecimal

Binary

11111111

Octal

377

How Hexadecimal Numbers Work

Hexadecimal (hex) is a base-16 positional number system that uses sixteen distinct symbols: the digits 0-9 represent values zero through nine, and the letters A-F represent values ten through fifteen. Each position in a hex number represents a power of 16, following the same place-value principle as the decimal (base-10) system. According to the IEEE, hexadecimal notation became the standard for representing binary data in computing because each hex digit maps to exactly 4 binary bits, making it a compact and human-readable shorthand for machine-level values. Web developers, systems programmers, and network engineers use hex daily for tasks ranging from binary data manipulation to CSS color codes.

How Hex Conversion Works

To convert a hexadecimal number to decimal, multiply each digit by 16 raised to the power of its position (counting from 0 on the right), then sum the results. The formula is:

Decimal = d(n) x 16^n + d(n-1) x 16^(n-1) + ... + d(1) x 16^1 + d(0) x 16^0

d(i) — the value of the hex digit at position i (A=10, B=11, C=12, D=13, E=14, F=15)
16^i — the base (16) raised to the position power

Worked example: Convert hex 2F3 to decimal. 2 x 16^2 + F(15) x 16^1 + 3 x 16^0 = 2 x 256 + 15 x 16 + 3 x 1 = 512 + 240 + 3 = 755. To convert back, repeatedly divide by 16: 755 / 16 = 47 remainder 3, 47 / 16 = 2 remainder 15 (F), 2 / 16 = 0 remainder 2, reading remainders bottom-up gives 2F3.

Key Terms You Should Know

Base / Radix — the number of unique digits in a number system. Hex is base-16, decimal is base-10, binary is base-2, and octal is base-8.
Nibble — a group of 4 bits, exactly one hex digit. A byte (8 bits) consists of two nibbles, represented by two hex digits (e.g., FF = 11111111 in binary).
0x Prefix — a common notation in programming languages (C, Java, Python) to indicate a hex literal, e.g., 0xFF equals decimal 255.
Hex Color Code — a six-digit hex value used in CSS/HTML to define colors, where pairs represent red, green, and blue channels (e.g., #FF5733).
Two's Complement — a method for representing signed integers in binary/hex. In an 8-bit system, hex FF represents -1 in signed interpretation.

Number Base Comparison Table

The table below shows equivalent values across the four most common number bases used in computing, as defined by the ISO/IEC 9899 C standard.

Decimal	Hexadecimal	Binary	Octal	Common Use
0	0	0000	0	Null byte
10	A	1010	12	Line feed (ASCII)
127	7F	01111111	177	Max signed 8-bit int
255	FF	11111111	377	Max unsigned 8-bit int
65535	FFFF	1111111111111111	177777	Max unsigned 16-bit int
16777215	FFFFFF	24 bits all 1s	77777777	White (#FFFFFF)

Practical Hex Conversion Examples

Example 1 — CSS color code: The color coral is defined as #FF7F50 in hex. Breaking it down: Red = FF (255), Green = 7F (127), Blue = 50 (80). Each pair of hex digits represents a color channel value from 0-255. To darken this color by 20%, multiply each channel by 0.8: Red = CC (204), Green = 66 (102), Blue = 40 (64), giving #CC6640.

Example 2 — Memory address: A 32-bit memory address 0x0040F000 in hex equals 4,255,744 in decimal. Programmers use hex because it is far more readable than the binary equivalent 00000000010000001111000000000000. Use our scientific calculator for additional computational needs.

Example 3 — Hex arithmetic: Adding hex 1A3 + 2BC: convert to decimal (419 + 700 = 1119), then back to hex = 45F. Alternatively, add column by column in base 16: 3 + C = F, A + B = 15 (write 5, carry 1), 1 + 2 + 1 = 4, result = 45F.

Tips for Working with Hexadecimal

Memorize the hex-binary mapping: Each hex digit maps to a unique 4-bit pattern (0=0000, 1=0001, ..., F=1111). Knowing these 16 pairs by heart makes conversions instant.
Use the 0x prefix consistently: In code, always prefix hex values with 0x to avoid ambiguity. The value 10 is decimal ten, while 0x10 is decimal sixteen.
Group binary digits in fours: When converting binary to hex, pad the leftmost group with zeros to make a full nibble, then convert each group: 110101 becomes 0011 0101 = 35.
Leverage hex for debugging: Most debuggers and memory viewers display data in hex by default. A percentage calculator can help when analyzing utilization rates in hex-based memory dumps.
Check your work with complements: In 8-bit hex, a number and its two's complement should sum to 100 (decimal 256). For example, 3A + C6 = 100.

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