In this tutorial, we will learn how to convert decimal numbers to binary numbers quickly. We will cover the conversion process for both integers and fractions.

Converting an Integer from Decimal to Binary:

To convert a decimal integer to binary, follow these steps:

  1. Divide the decimal number by 2.
  2. Take note of the remainder.
  3. Repeat steps 1 and 2 with the quotient until you reach zero.
  4. Reverse the sequence of remainders to obtain the binary representation of the decimal number.

For example, let’s convert the decimal number 29 to binary:

29 ÷ 2 = 14 with a remainder of 1 14 ÷ 2 = 7 with a remainder of 0 7 ÷ 2 = 3 with a remainder of 1 3 ÷ 2 = 1 with a remainder of 1 1 ÷ 2 = 0 with a remainder of 1

The binary representation of 29 is 11101.

Let’s look at another example. Converting the decimal number 145 to binary:

145 ÷ 2 = 72 with a remainder of 1 72 ÷ 2 = 36 with a remainder of 0 36 ÷ 2 = 18 with a remainder of 0 18 ÷ 2 = 9 with a remainder of 0 9 ÷ 2 = 4 with a remainder of 1 4 ÷ 2 = 2 with a remainder of 0 2 ÷ 2 = 1 with a remainder of 0 1 ÷ 2 = 0 with a remainder of 1

The binary representation of 145 is 10010001.

Converting a Fraction from Decimal to Binary:

To convert the decimal part of a fraction to binary, follow these steps:

  1. Multiply the fractional part by 2.
  2. Take note of the integer part of the result.
  3. Repeat steps 1 and 2 until the fractional part becomes 0.
  4. Read the sequence of integers obtained from top to bottom.
  5. Combine the integer part and the fractional part to obtain the binary representation of the fraction.

For example, let’s convert the fraction 0.375 to binary:

0.375 × 2 = 0.75, integer part = 0 0.75 × 2 = 1.5, integer part = 1 0.5 × 2 = 1, integer part = 1

The binary representation of 0.375 is 0.011.

Finally, combine the integer part (0) and the fractional part (0.011) to get the binary representation of the entire number.

The number 0.375 converted to binary is 0.011.

By learning the process of converting decimal numbers to binary, you can gain a better understanding of how binary numbers work and communicate with computers.