Hex to Binary converter

What is a Hexadecimal Number?

A hexadecimal number, often abbreviated as "hex," is a number system with a base of 16. Unlike the decimal system (base-10), which uses the digits 0-9, hexadecimal uses the following 16 symbols:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

- 0-9 represent the decimal values 0 to 9.
- A-F represent the decimal values 10 to 15.

Hexadecimal is widely used in computing and digital systems because it is more compact than binary (base-2) and easier for humans to read and write. It is commonly used to represent memory addresses, colors in web design, and binary data.

Example:

1. The hexadecimal number 1A3F can be converted to decimal as follows:
   1 × 16³ + 10 × 16² + 3 × 16¹ + 15 × 16⁰ = 6703 in decimal.

What is a Binary Number?

A binary number is a number expressed in the base-2 numeral system, which uses only two symbols: 0 and 1. Each digit in a binary number is referred to as a bit. Binary numbers are the foundation of digital systems and computing because they align directly with the on/off states of transistors in electronic devices.

In the binary system:
- 0 represents the "off" state.
- 1 represents the "on" state.

Binary numbers are used in various applications, including arithmetic operations in computers, data storage, and network protocols.

Example:

1. The binary number 1011 can be converted to decimal as follows:
   1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰ = 8 + 0 + 2 + 1 = 11

How to Convert Hexadecimal to Binary?

Converting a hexadecimal (hex) number to binary is a straightforward process because each hex digit corresponds to exactly 4 binary digits (bits). This is due to the fact that the base-16 system (hex) can represent 16 values, which aligns perfectly with the 16 combinations of 4 binary bits (2⁴ = 16).

Steps for Conversion:

1. Write the Hex Number: Start with the hexadecimal number you want to convert.
2. Replace Each Hex Digit: Convert each hex digit into its 4-bit binary equivalent using a conversion table.
3. Combine the Binary Groups: Write down all the binary groups in the same order as the hex digits to form the full binary number.

Hex to Binary Conversion Table:

Example Conversion:

Convert the hex number 2F3 to binary:

1. Write each hex digit:
   • 2 → 0010
   • F → 1111
   • 3 → 0011
2. Combine the binary groups:2F3 (hex) = 0010 1111 0011 (binary)