Hex to Binary Converter
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.