How to convert Hexadecimal to Binary?

Step-by-Step Hexadecimal to Binary Conversion Guide

Learning hexadecimal to binary conversion is essential for anyone working with computers or digital systems. Fortunately, there’s a direct relationship that makes this process straightforward.

Simple Hexadecimal to Binary Conversion Steps Anyone Can Follow

The key insight that makes hex-to-binary conversion easy is this: Each hex digit corresponds to exactly four binary digits (bits).

Here’s how to convert any hexadecimal number to binary:

1. Break down the hex number into individual digits
2. Convert each hex digit to its 4-bit binary equivalent
3. Combine all the binary groups to get your final answer

That’s it! No complex math required.

Complete Hexadecimal to Binary Table for Quick Reference

A hexadecimal to binary table is an invaluable reference tool that shows the 4-bit binary equivalent of each hex digit. Here’s a complete conversion table you can use:

Hex	Binary	Hex	Binary
0	0000	8	1000
1	0001	9	1001
2	0010	A	1010
3	0011	B	1011
4	0100	C	1100
5	0101	D	1101
6	0110	E	1110
7	0111	F	1111

With this table, you can quickly look up the binary equivalent of any hex digit. This makes the conversion process much faster once you’ve practised a few times.

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In this guide, I’ll walk you through this conversion process in a way that’s easy to grasp, even if you’re new to these number systems. By the end, you’ll be converting hex to binary with confidence!

Understanding the Hexadecimal Number System

The hexadecimal number system (also called hex) is a base-16 system that uses 16 different symbols to represent values. These include:

• The digits 0-9 (representing values zero through nine)
• The letters A-F (representing values ten through fifteen)

For example, in hexadecimal:

• A = 10 in decimal
• B = 11 in decimal
• F = 15 in decimal

This system is widely used in computing because it provides a more compact way to represent binary data. The hexadecimal number system makes it much easier to work with large binary numbers that would otherwise be unwieldy.

What is the Binary Number System?

The binary number system is a base-2 system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from the rightmost digit (2⁰ = 1) and increasing as you move left (2¹ = 2, 2² = 4, 2³ = 8, and so on).

For example, the binary number 1011 equals:

• 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰
• 8 + 0 + 2 + 1 = 11 in decimal

The binary number system forms the foundation of all computing because electronic components can easily represent two states: on/off or high/low voltage.

Practical Hex to Binary Conversion Examples

Let’s work through some examples to see how the hex to binary process is straightforward once you understand the relationship between these number systems.

Example 1: Convert A3 to binary

1. Breakdown: A and 3
2. Convert using the table:
   • A = 1010
   • 3 = 0011
3. Combine: 1010 0011

So, A3₁₆ = 10100011₂

Example 2: Convert 7B to binary

1. Breakdown: 7 and B
2. Convert using the table:
   • 7 = 0111
   • B = 1011
3. Combine: 0111 1011

So, 7B₁₆ = 01111011₂ (or simply 1111011₂ if we drop the leading zero)

Example 3: Convert 1F4 to binary

1. Break down: 1, F, and 4
2. Convert using the table:
   • 1 = 0001
   • F = 1111
   • 4 = 0100
3. Combine: 0001 1111 0100

So, 1F4₁₆ = 000111110100₂ (or 111110100₂ without leading zeros)

How to Convert Hexadecimal with Decimal Points to Binary

For hex numbers with decimal points (like 5A.C3), follow these steps:

1. Split the number at the decimal point
2. Convert each part separately using the same method
3. Recombine with the binary point in the same position

For example, to convert 5A.C3:

• 5 = 0101, A = 1010, so 5A = 0101 1010
• C = 1100, 3 = 0011, so C3 = 1100 0011
• Result: 5A.C3₁₆ = 0101 1010.1100 0011₂

Why Number System Conversion Matters in Computing

Understanding number system conversion skills is crucial for anyone working in computer science or digital electronics. Here’s why hexadecimal to binary conversion is particularly useful:

• Memory and addressing: Computer memory addresses are often represented in hex for readability, but the computer works with them in binary
• Colour codes: Web developers use hex codes for colours (like #FF5733), which are binary values for RGB components
• Debugging: When debugging low-level code or examining memory dumps, you’ll frequently need to convert between hex and binary
• Digital design: Hardware engineers use hex as shorthand for binary patterns when designing digital circuits
• Data representation: Hex provides a compact way to represent binary data in a human-readable format

The base-16 number system provides a perfect balance between human readability and computer efficiency, which is why it’s so widely used in computing.

Frequently Asked Questions

Conclusion

Converting hexadecimal to binary doesn’t have to be complicated. By understanding that each hex digit represents exactly four binary digits, you can quickly convert any hex number to its binary equivalent.

Remember the simple three-step process:

1. Break down the hex number into individual digits
2. Convert each digit to its 4-bit binary equivalent
3. Combine all the binary groups

With a bit of practice, you’ll be converting between these number systems with ease. And for those times when you need to convert complex numbers quickly, try the Hexadecimal to Binary Converter tool on AiCalculator.It’s free, fast, and accurate!