Convert Decimal, Binary, Hexadecimal, and Octal Numbers

How can you convert a decimal number to binary and hexadecimal?

a) Decimal to binary

b) Decimal to hexadecimal

Conversion Process:

a) To convert a decimal number to binary, use the repeated division-by-2 method and read the remainders in reverse order.

b) To convert a decimal number to hexadecimal, use the repeated division-by-16 method.

Converting decimal numbers to binary and hexadecimal involves specific methods that allow you to represent the numbers in different systems.

Decimal to Binary Conversion:

To convert a decimal number to binary, you can use the repeated division-by-2 method. Divide the decimal number by 2 and write down the remainder. Continue dividing the quotient by 2 until the quotient is 0. Read the remainders in reverse order to obtain the binary representation.

For example, to convert the decimal number 14 to binary:

14 ÷ 2 = 7 remainder 0

7 ÷ 2 = 3 remainder 1

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

The binary representation of 14 is 1110.

Decimal to Hexadecimal Conversion:

To convert a decimal number to hexadecimal, you can use the repeated division-by-16 method. Divide the decimal number by 16 and write down the remainder. Continue dividing the quotient by 16 until the quotient is 0. Replace any remainders greater than 9 with their corresponding hexadecimal letters.

For example, to convert the decimal number 256 to hexadecimal:

256 ÷ 16 = 16 remainder 0

16 ÷ 16 = 1 remainder 0

1 ÷ 16 = 0 remainder 1

The hexadecimal representation of 256 is 100.