Binary to Hexadecimal Conversion

Binary is the simple number system that uses only two digits of 0 and 1 (i.e. value of base 2). Whereas Hexadecimal(Hex) number is one of the number systems which has a value is 16 and it contains only 16 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F.

The number system also has a Binary to Hex Converter. The four number systems used in math are binary, octal, decimal, and Hexa-decimal. Each form may be changed to the alternative number system using the conversion table. Now we move ahead into Binary to Hex Converter.

To better understand, let's look at the methods for changing binary numbers to Hexa-decimal ones. This is one of the easiest topics that we are going to cover. This is one of the easiest topics we will explore. Now we move forward into Binary to Hex Converter.

Binary

A binary number is a number expressed in the base 2 numeral system. Binary number's digits have 2 symbols: zero (0) and one (1). Each digit of a binary number counts a power of 2.

Binary number example:

1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀

Hexadecimal

A hexadecimal number is a number expressed in the base 16 numeral system. Hexadecimal number's digits have 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Each digit of a hexadecimal number counts a power of 16.

Hexadecimal number example:

62C₁₆ = 6×16² + 2×16¹ + 12×16⁰ = 1580₁₀

Example

Understanding Binary-to-Hexadecimal Conversion

Binary-to-hexadecimal conversion involves converting numbers from base 2 (binary) to base 16 (hexadecimal). Binary numbers are composed of 0s and 1s, while hexadecimal numbers are composed of digits from 0 to 9 and letters A to F (representing values 10 to 15).

The general approach to converting binary numbers to hexadecimal includes:

Grouping binary digits into sets of four, starting from the right (add leading zeros if necessary).
Converting each group of four binary digits to their equivalent hexadecimal digit.
Writing the hexadecimal digits in sequence to form the final hexadecimal number.

Steps for Binary-to-Hexadecimal Conversion

Step 1: Divide the binary number into groups of four digits starting from the right. Add leading zeros to complete groups if needed.

Step 2: Convert each group of four binary digits into the corresponding hexadecimal digit.

Step 3: Combine the hexadecimal digits to form the final result.

Example: Converting Binary to Hexadecimal

Convert \( 101101 \) to hexadecimal:

Group the binary digits into sets of four: \( 101101 \) becomes \( 0010 \, 1101 \) (add leading zeros).
Convert each group to hexadecimal: \( 0010 → 2 \), \( 1101 → D \).
Final hexadecimal result: \( 2D \).

Conversion Table for Quick Reference

Here is a quick reference for converting binary to hexadecimal:

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

Applications of Binary-to-Hexadecimal Conversion

Binary-to-hexadecimal conversion is commonly used in:

Computer programming and systems for simplifying binary data representation.
Representing memory addresses and machine-level instructions.
Digital electronics for compact and readable data representation.

Practice Problem

Convert \( 11001110 \) to hexadecimal:

Solution: Group the digits: \( 1100 \, 1110 \) (no leading zeros required).
Convert each group: \( 1100 → C \), \( 1110 → E \).
Final hexadecimal result: \( CE \).

Binary-to-Hexadecimal Conversion Examples Table
Problem Type	Description	Steps to Solve	Example
Basic Conversion	Converting a binary number to its hexadecimal equivalent.	Group the binary digits in sets of four, starting from the right. Convert each group of four binary digits into its decimal equivalent, then map to the corresponding hexadecimal value.	For \( 110010 \): Group: Add leading zeros to make \( 0011 \) and \( 0010 \). Convert: \( 0011 = 3 \), \( 0010 = 2 \). Result: \( 32 \) in hexadecimal.
Adding Leading Zeros	Ensuring the binary number has groups of four by adding leading zeros.	If the number of binary digits is not a multiple of four, add zeros to the left until it is. Follow the basic conversion process.	For \( 10101 \): Add leading zeros: \( 0001 \) and \( 0101 \). Convert: \( 0001 = 1 \), \( 0101 = 5 \). Result: \( 15 \) in hexadecimal.
Handling Larger Numbers	Converting longer binary numbers by grouping into fours.	Split the binary number into groups of four from the right. Convert each group independently.	For \( 111001110 \): Add leading zero: \( 0001 \) and group as \( 1100 \), \( 1110 \). Convert: \( 0001 = 1 \), \( 1100 = C \), \( 1110 = E \). Result: \( 1CE \) in hexadecimal.
Verifying Conversion	Checking the accuracy of binary-to-hexadecimal conversion.	Convert the hexadecimal result back to binary by replacing each hexadecimal digit with its 4-bit binary equivalent. Ensure the original binary number matches.	For \( 110010 \) (converted to \( 32 \) in hexadecimal): Convert \( 3 \) to \( 0011 \) and \( 2 \) to \( 0010 \). Combine: \( 0011 \) and \( 0010 \) to get \( 110010 \). Matches the original binary number.
Applications	Understanding where binary-to-hexadecimal conversion is used.	Hexadecimal is widely used in programming and debugging for representing memory addresses and machine code. It provides a compact and human-readable representation of binary data.	Example: Converting binary data in computer systems to hexadecimal for better readability in debugging tools.