Hex to Binary Converter



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Converting a Hexadecimal Number to Binary

Hexadecimal (hex) and binary are both numeral systems used extensively in computing. The hexadecimal system (base-16) uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F (or a-f) to represent values ten to fifteen. The binary system (base-2) uses only two digits: 0 and 1. Hexadecimal numbers are often used to represent binary values more compactly because each hex digit corresponds to exactly four binary digits (bits).

To convert a hexadecimal number to its binary equivalent, each hex digit is replaced with its corresponding 4-bit binary value. This makes the conversion straightforward and ensures that the resulting binary number accurately represents the original hex number.

For example, the hexadecimal number 1A3 can be converted to binary by converting each digit individually:

1 = 0001, A = 1010, 3 = 0011

Therefore, the binary equivalent of 1A3 is 000110100011.

Examples

Let’s explore some examples to understand how to convert hexadecimal numbers to their binary equivalents.

1. Convert the hexadecimal number 1A3 to binary.

Answer

First, we identify the given number:

Given:

  • Hexadecimal: 1A3

Next, we convert each hex digit to its corresponding 4-bit binary value:

Steps:

  • 1 = 0001
  • A = 1010
  • 3 = 0011

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

000110100011

Result:

∴ The binary equivalent of the hexadecimal number 1A3 is 000110100011.

2. Convert the hexadecimal number 4F to binary.

Answer

We start by identifying the number:

Given:

  • Hexadecimal: 4F

Next, we convert each hex digit to its corresponding 4-bit binary value:

Steps:

  • 4 = 0100
  • F = 1111

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

01001111

Result:

∴ The binary equivalent of the hexadecimal number 4F is 01001111.

3. Determine the binary equivalent of the hexadecimal number B7.

Answer

First, we identify the given number:

Given:

  • Hexadecimal: B7

Next, we convert each hex digit to its corresponding 4-bit binary value:

Steps:

  • B = 1011
  • 7 = 0111

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

10110111

Result:

∴ The binary equivalent of the hexadecimal number B7 is 10110111.

4. Convert the hexadecimal number 2C to binary.

Answer

We start by identifying the number:

Given:

  • Hexadecimal: 2C

Next, we convert each hex digit to its corresponding 4-bit binary value:

Steps:

  • 2 = 0010
  • C = 1100

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

00101100

Result:

∴ The binary equivalent of the hexadecimal number 2C is 00101100.