Binary to Hexadecimal Converter

Convert Binary to Hexadecimal

Enter a binary number below to convert it to hexadecimal. Our converter handles binary numbers of any length.

Please enter a valid binary number (0s and 1s only).

How to Convert Binary to Hexadecimal

Converting binary numbers to hexadecimal is a common task in computer science and digital systems. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

The conversion from binary to hexadecimal involves two steps:

  1. Convert binary to decimal
  2. Convert decimal to hexadecimal

For binary to decimal conversion:

\[ (b_n b_{n-1} ... b_1 b_0)_2 = b_n \times 2^n + b_{n-1} \times 2^{n-1} + ... + b_1 \times 2^1 + b_0 \times 2^0 \]

Where:

  • \(b_i\) represents each digit of the binary number (0 or 1)
  • \(n\) is the position of the digit (starting from 0 for the rightmost digit)

Conversion Steps

  1. Group the binary digits into sets of four, starting from the right.
  2. Convert each group of four binary digits to its hexadecimal equivalent.
  3. Combine the hexadecimal digits to form the final result.

Example Conversion

Let's convert the binary number 1010111100001001 to hexadecimal.

Step 1: Group Binary Digits

1010 1111 0000 1001

Step 2: Convert Each Group

1010 = A

1111 = F

0000 = 0

1001 = 9

Step 3: Combine Results

Therefore, 1010111100001001 in binary = AF09 in hexadecimal

Visual Representation

Binary to Hexadecimal Conversion Process 1010 1111 0000 1001 Binary Input (Grouped in 4 bits) Conversion Steps 1010 = 10 = A 1111 = 15 = F 0000 = 0 1001 = 9 8+2=10 8+4+2+1=15 0+0+0+0=0 8+0+0+1=9 2³ 2² 2¹ 2⁰ 2³ 2² 2¹ 2⁰ 2³ 2² 2¹ 2⁰ 2³ 2² 2¹ 2⁰ AF09 Hexadecimal Result

This diagram illustrates the process of converting the binary number 1010111100001001 to its hexadecimal equivalent AF09.

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