Binary to Hexadecimal

Binary and hexadecimal number systems are fundamental in the field of computer science and digital electronics. While binary (base-2) is the language of computers, hexadecimal (base-16) offers a more compact and readable representation of binary values. Understanding how to convert binary numbers to hexadecimal is crucial for programming, debugging, and working with computer memory. This article provides a detailed explanation of the conversion process, along with examples to illustrate each step.

Understanding the Number Systems

Binary System

The binary system is a base-2 number system that uses only two symbols: 0 and 1. Each digit in a binary number represents a power of 2, starting from $2^0$ on the right.

Hexadecimal System

The hexadecimal system is a base-16 number system that uses sixteen symbols: 0-9 for values zero to nine, and A-F (or a-f) for values ten to fifteen. Each digit in a hexadecimal number represents a power of 16, starting from $16^0$ on the right.

Conversion Process

Converting a binary number to a hexadecimal number involves grouping the binary digits and translating each group into its hexadecimal equivalent. Here are the steps:

1. Group the binary digits into sets of four: Start from the right (least significant digit). Add leading zeros if necessary to complete the last group.
2. Convert each group of four binary digits to its hexadecimal equivalent: Use a binary to hexadecimal conversion chart.
3. Combine the hexadecimal digits: Write the hexadecimal digits together to form the final hexadecimal number.

Example: Converting Binary to Hexadecimal

Let’s convert the binary number 110101101011 to hexadecimal.

1. Group the binary digits into sets of four:

   • Starting from the right: 1101 0110 1011
   • If necessary, add leading zeros to the leftmost group to complete four digits: No need in this case, as all groups are already complete.

2. Convert each group of four binary digits to its hexadecimal equivalent:

   • 1101 in binary is D in hexadecimal (8+4+0+1 = 13, which is D).
   • 0110 in binary is 6 in hexadecimal (0+4+2+0 = 6).
   • 1011 in binary is B in hexadecimal (8+0+2+1 = 11, which is B).

3. Combine the hexadecimal digits:

   • The hexadecimal representation of 110101101011 is D6B.

Another Example: Converting 101011110001 to Hexadecimal

1. Group the binary digits into sets of four:

   • Starting from the right: 1011 1110 0001
   • No need to add leading zeros, as all groups are already complete.

2. Convert each group of four binary digits to its hexadecimal equivalent:

   • 1011 in binary is B in hexadecimal (8+0+2+1 = 11