How Binary to Hexadecimal Conversion Works

Converting from binary to hexadecimal is a fundamental operation in computing. Here's a step-by-step explanation:

Step 1: Group Binary Digits

First, we group the binary digits into sets of 4 bits, starting from the right. If the leftmost group doesn't have 4 digits, we pad it with leading zeros.

Step 2: Convert Each Group to Hexadecimal

Each 4-bit group corresponds to a single hexadecimal digit:

Step 3: Combine the Hexadecimal Digits

Finally, join the hexadecimal digits in the same order:

Hexadecimal to Binary Conversion

To convert from hexadecimal to binary, we reverse the process:

1. Convert each hexadecimal digit to its 4-bit binary equivalent
2. Combine the binary groups in the same order

Signed Binary Numbers

When dealing with signed binary numbers, we use two's complement representation:

• Positive numbers are represented normally
• Negative numbers: invert all bits and add 1

For example, -5 in 8-bit binary:

1. 5 in binary: 00000101
2. Invert all bits: 11111010
3. Add 1: 11111011

So -5 in 8-bit two's complement is 11111011, which converts to FB in hexadecimal.