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:

**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.**Convert each group of four binary digits to its hexadecimal equivalent**: Use a binary to hexadecimal conversion chart.**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.

**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.

- Starting from the right:
**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).

**Combine the hexadecimal digits**:- The hexadecimal representation of
`110101101011`

is`D6B`

.

- The hexadecimal representation of

### Another Example: Converting `101011110001`

to Hexadecimal

**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.

- Starting from the right:
**Convert each group of four binary digits to its hexadecimal equivalent**:`1011`

in binary is`B`

in hexadecimal (8+0+2+1 = 11