Hexadecimal, often shortened to “hex,” is a base-16 number system used in mathematics and computing. It uses 16 symbols to represent values: the numbers 0 to 9 and the letters A to F. Each hex digit represents four binary digits (bits), making it a convenient way to express binary numbers in a more compact and readable form.

Here are the key points about hexadecimal:
Hexadecimal Digits:

0-9: Represent values 0 to 9.
A-F: Represent values 10 to 15.

Hexadecimal to Decimal Conversion:

To convert a hexadecimal number to decimal, multiply each hex digit by 16 raised to the power of its position (starting from 0) from right to left.

Example:

Decimal to Hexadecimal Conversion:

To convert a decimal number to hexadecimal, repeatedly divide the number by 16 and record the remainders. The remainders, read in reverse order, form the hex number.

Example:
Convert 675 to hexadecimal:

675 ÷ 16 = 42 remainder 3
42 ÷ 16 = 2 remainder 10 (A)
2 ÷ 16 = 0 remainder 2

Reading the remainders from bottom to top, we get:
675=2A3 (hex)675=2A3(hex)
Binary to Hexadecimal Conversion:

To convert binary to hex, group the binary digits into sets of four (starting from the right). Then, convert each group to its hex equivalent.

Example:
Binary 110101111:

Group into sets of four: 0110 1011 1 (pad with leading zeros if necessary: 0110 1011 0001)
Convert each group to hex: 6 B 1

So, 110101111 in binary is 6B1 in hexadecimal.
Hexadecimal in Computing:

Memory Addresses: Hex is often used to represent memory addresses.
Colors in Web Design: Hex codes are used to specify colors in web design (e.g., #FFFFFF for white).
Machine Code: Instructions and data in low-level programming and debugging are often displayed in hexadecimal.

Summary Table:
Decimal Binary Hexadecimal
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F

Understanding hexadecimal is crucial in many areas of computer science and digital electronics, providing a more human-readable way to handle binary numbers.

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