How to do hex-to-binary and binary-to-hex conversion?

Converting between hexadecimal (hex) and binary is a common task in programming and digital electronics, involving the translation of numbers between base 16 (hexadecimal) and base 2 (binary) systems. Each hex digit directly corresponds to a 4-bit binary digit, making the conversion straightforward.

Hexadecimal to Binary Conversion

To convert a hexadecimal number to binary:

1. Replace each hex digit with its equivalent 4-bit binary value.

Hex to Binary Mapping:

• 0 → 0000
• 1 → 0001
• 2 → 0010
• 3 → 0011
• 4 → 0100
• 5 → 0101
• 6 → 0110
• 7 → 0111
• 8 → 1000
• 9 → 1001
• A → 1010
• B → 1011
• C → 1100
• D → 1101
• E → 1110
• F → 1111

Example: Convert Hex 1A3 to Binary

• 1 → 0001
• A → 1010
• 3 → 0011 Result: 1A3 in hex is 000110100011 in binary.

Binary to Hexadecimal Conversion

To convert a binary number to hexadecimal:

1. Split the binary number into groups of four bits. Start from the right (least significant bits). If the leftmost group has less than four bits, pad it with zeros.
2. Replace each group of four bits with the corresponding hex digit.

Example: Convert Binary 110101110101 to Hex

1. Split into groups: 1101 0111 0101
2. Convert each group:
   • 1101 → D
   • 0111 → 7
   • 0101 → 5 Result: 110101110101 in binary is D75 in hex.

Practical Methods for Conversion in Programming

In Python

Python provides built-in functions to handle these conversions:

• hex() converts an integer to a hexadecimal string.
• bin() converts an integer to a binary string.
• You can also use format strings or the format() function for more control over formatting.

# Hex to Binary
hex_number = "1A3"
binary_number = bin(int(hex_number, 16))[2:]  # Convert hex to integer to binary
print("Hex to Binary:", binary_number)

# Binary to Hex
binary_number = "110101110101"
hex_number = hex(int(binary_number, 2))[2:]  # Convert binary to integer to hex
print("Binary to Hex:", hex_number.upper())

In JavaScript

JavaScript also provides methods for these conversions, utilizing the parseInt() and toString() methods.

// Hex to Binary
const hexNumber = "1A3";
const binaryNumber = parseInt(hexNumber, 16).toString(2);
console.log("Hex to Binary:", binaryNumber);

// Binary to Hex
const binaryNumber = "110101110101";
const hexNumber = parseInt(binaryNumber, 2).toString(16).toUpperCase();
console.log("Binary to Hex:", hexNumber);

Conclusion

Hex-to-binary and binary-to-hex conversions are straightforward due to the direct correspondence between hex digits and binary quartets. This makes the conversions easy to perform manually and programmatically. Such conversions are especially useful in fields like computer science, where binary and hexadecimal are used extensively to represent and manipulate data at low levels.