# Decimal, Binary, and Hexadecimal Conversion

## How do we convert numbers between decimal, binary, and hexadecimal?

Let's explore the conversion process for different number systems.

## Answer:

Converting numbers between decimal, binary, and hexadecimal involves understanding the positional numeral systems and their relationships. Here's how we can perform these conversions:

## Conversion Process:

**1. Decimal to Binary:** To convert a decimal number to binary, we repeatedly divide the decimal number by 2 and record the remainders in reverse order.

**2. Decimal to Hexadecimal:** To convert a decimal number to hexadecimal, we divide the decimal number by 16 successively and record the remainders in reverse order. Certain remainders are represented by hex symbols.

**3. Binary to Decimal:** To convert a binary number to decimal, we multiply each bit by 2 raised to the power of its position and sum the results.

**4. Binary to Hexadecimal:** To convert a binary number to hexadecimal, we group the binary number into sets of 4 bits each and substitute each 4-bit group with its hexadecimal equivalent.

**5. Hexadecimal to Decimal:** To convert a hexadecimal number to decimal, we multiply each digit by 16 raised to the power of its position and sum the results.

**6. Hexadecimal to Binary:** To convert a hexadecimal number to binary, we replace each digit with its 4-bit binary equivalent.

By understanding these conversion methods, we can easily switch between decimal, binary, and hexadecimal numbers.