Hexadecimal to Binary Converter
Convert hexadecimal numbers to binary numbers easily and accurately.
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Table of Contents
History and Importance of Hexadecimal
Origins and Evolution
The hexadecimal (base-16) number system has a rich history dating back to the 17th century when mathematician Gottfried Wilhelm Leibniz first conceived it around 1679. Contrary to popular belief, Leibniz, not Swedish-American engineer John William Nystrom, was the original inventor of base 16. Leibniz explored various notations, including using Roman letters m, n, p, q, r, and s for the six extra digits required beyond 0-9.
The term "hexadecimal" itself wasn't popularized until the 1950s, when the National Bureau of Standards (now known as the National Institute of Standards and Technology) used it for the Standards Eastern Automatic Computer (SEAC). They established the now-standard notation of using 0-9 and A-F as the sixteen digits, which has remained the convention ever since.
Throughout history, various terms have been used for base 16, including sedecimal, sexdecimal, sedenary, and senidenary. The term "hexadecimal" is actually a hybrid of Greek and Latin roots (Greek "hex" for six and Latin "decimal" for ten), making it etymologically impure, though now universally accepted.
Why Hexadecimal Matters in Computing
Hexadecimal's true significance emerged with the advent of modern computing. The relationship between hexadecimal and binary is what makes it particularly valuable in computer science:
- Efficient Binary Representation: Each hexadecimal digit perfectly represents four binary digits (bits), making it an incredibly compact way to express binary data. For example, the binary number 1010110110001010 can be written much more concisely as AB8A in hexadecimal.
- Memory Addresses: Computer memory locations are commonly expressed in hexadecimal, as they provide a more human-readable format than long strings of binary digits.
- Color Codes: Web developers use hexadecimal daily in CSS color codes (like #FF5733), where each pair of hex digits represents the intensity of red, green, and blue components.
- Assembly Language: Low-level programming often involves hexadecimal notation for memory addresses, op-codes, and immediate values.
- Debugging: Hexadecimal is used in debugging tools and memory dumps to display binary data in a more readable format.
- Network Addresses: MAC addresses and IPv6 addresses use hexadecimal notation for compact representation.
Modern Applications
Today, hexadecimal is essential in various computing contexts:
Digital Security
Cryptographic keys, hash values, and digital signatures are commonly represented in hexadecimal.
File Formats
Binary file formats often use hexadecimal for magic numbers and structure definitions.
Hardware Programming
Microcontroller and embedded system programming frequently use hex for device registers and memory operations.
Digital Media
Binary data in images, audio, and video files is often represented and manipulated in hexadecimal form.
Did you know? The common computer notation "0x" used to prefix hexadecimal numbers (such as 0x1A3F) became widespread through the C programming language, though its origins may trace back to earlier IBM systems.
Understanding the relationship between hexadecimal and binary is essential for anyone working in computer science, programming, or digital electronics. Converting between these number systems is a fundamental skill that provides insight into how computers actually store and process information.
How to Convert Hexadecimal to Binary
Hexadecimal (base-16) uses the following digits:
0-9
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
Steps to Convert:
-
1Convert each hexadecimal digit to its 4-bit binary equivalent
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2Combine all the binary digits in order
1A = 0001 1010
1 = 0001
A = 1010
Hexadecimal to Binary Conversion Table:
0 = 0000
1 = 0001
2 = 0010
3 = 0011
4 = 0100
5 = 0101
6 = 0110
7 = 0111
8 = 1000
9 = 1001
A = 1010
B = 1011
C = 1100
D = 1101
E = 1110
F = 1111
Common Examples
Example 1 Basic Numbers
0x0 = 0000
0x1 = 0001
0x9 = 1001
Example 2 Letters
0xA = 1010
0xF = 1111
0xFF = 11111111
Example 3 Common Values
0x10 = 00010000
0x100 = 000100000000
0x1000 = 0001000000000000
Example 4 Mixed Numbers
0x1A = 00011010
0xB4 = 10110100
0x3E8 = 001111101000