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.