How to Convert Binary (Base 2) to Hexadecimal?

To convert a binary number (base 2) to a hexadecimal number (base 16), you group the binary digits into sets of four, starting from the rightmost digit. Then, you convert each group of four binary digits into its corresponding hexadecimal digit.

Step-by-Step Conversion

Here's a detailed breakdown of the process:

1. Group the Binary Digits: Starting from the right, divide the binary number into groups of four digits. If the number of digits is not a multiple of four, add leading zeros to the leftmost group to make it a group of four.

2. Convert Each Group to Hexadecimal: Use the following table to convert each group of four binary digits into its hexadecimal equivalent:

   Binary	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

3. Combine the Hexadecimal Digits: Concatenate the hexadecimal digits obtained in the previous step to get the final hexadecimal number.

Example

Let's convert the binary number 110101101 to hexadecimal:

1. Grouping: Divide the binary number into groups of four, starting from the right: 0001 1010 1101. We added leading zeros to the leftmost group.

2. Conversion: Convert each group to its hexadecimal equivalent:

   • 0001 = 1
   • 1010 = A
   • 1101 = D

3. Combining: Concatenate the hexadecimal digits: 1AD

Therefore, the binary number 110101101 is equal to the hexadecimal number 1AD.

Summary

Converting from binary to hexadecimal is a straightforward process of grouping binary digits into sets of four and then translating each group into its corresponding hexadecimal digit using a conversion table.