Binary to Hexadecimal Converter

Convert binary numbers to hexadecimal numbers easily and accurately.

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Enter a binary number (0-1)

Fundamentals

Understanding Number Systems

Number systems are foundational to computing and provide different ways to represent numerical values. Understanding them is essential for effective programming, computer science, and digital electronics.

What Are Number Systems?

A number system is a mathematical notation for representing numbers using digits or symbols in a consistent manner. Each system has a "base" that determines how many unique digits are used before place values shift.

Decimal (Base-10)

Our everyday number system using digits 0-9. Each position represents a power of 10.

Example: 358₁₀

= 3×10² + 5×10¹ + 8×10⁰

= 300 + 50 + 8

Binary (Base-2)

Computer's native language using only digits 0-1. Each position represents a power of 2.

Example: 1011₂

= 1×2³ + 0×2² + 1×2¹ + 1×2⁰

= 8 + 0 + 2 + 1 = 11₁₀

Hexadecimal (Base-16)

Uses digits 0-9 and letters A-F (representing 10-15). Each position represents a power of 16.

Example: 1A3₁₆

= 1×16² + 10×16¹ + 3×16⁰

= 256 + 160 + 3 = 419₁₀

Why Computer Systems Use Different Number Bases

Computers use binary because electronic components naturally exist in two states: on (1) and off (0). However, binary numbers can become very long and difficult for humans to work with efficiently.

The Relationship Between Binary and Hexadecimal

Hexadecimal serves as a compact representation of binary data, making it much easier for humans to read and work with:

  • Each hexadecimal digit represents exactly 4 binary digits (a nibble)
  • 4 binary digits can represent values from 0 to 15, matching the range of a single hex digit
  • This creates a perfect 4:1 compression ratio for representing binary information

Practical Applications

Programming

Memory addresses, color values (RGB), and bit manipulation in code often use hexadecimal notation.

Networking

MAC addresses and IPv6 addresses are written in hexadecimal format.

Computer Architecture

Low-level memory dumps, machine code, and debugging tools frequently use hexadecimal.

Digital Electronics

Hardware registers and configuration values are typically represented in binary or hexadecimal.

Binary-Hexadecimal Conversion Table

Decimal Binary Hexadecimal
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F
Guide

How to Convert Binary to Hexadecimal

To convert binary to hexadecimal, we group the binary digits into sets of 4 (starting from the right) and convert each group to its hexadecimal equivalent.

Steps to Convert:

  1. 1
    Group the binary digits into sets of 4, starting from the right
  2. 2
    Convert each group of 4 binary digits to its hexadecimal equivalent
  3. 3
    Combine all hexadecimal digits in order
Example:

11010 = 0001 1010

0001 = 1

1010 = A

Result: 1A

Binary to Hexadecimal Conversion Table:

0000 = 0

0001 = 1

0010 = 2

0011 = 3

0100 = 4

0101 = 5

0110 = 6

0111 = 7

1000 = 8

1001 = 9

1010 = A

1011 = B

1100 = C

1101 = D

1110 = E

1111 = F

Examples

Common Examples

Example 1 Basic Numbers

0 = 0

1 = 1

10 = 2

Example 2 Common Values

100 = 4

1000 = 8

10000 = 10

Example 3 Mixed Numbers

1010 = A

1100 = C

1111 = F

Example 4 Larger Numbers

10000 = 10

100000 = 20

1000000 = 40

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