Cracking the Code: Converting Fractional Decimal Numbers to Binary
Binary numbers are the language of computers, but they can seem like a foreign concept to many people. If you’re struggling to understand how to convert a fractional decimal number like 6.75 to binary, you’ve come to the right place. With a few simple steps, you’ll be able to “crack the code” and start understanding this important concept.
What Is a Binary Number?
Binary numbers are simply numbers that are expressed in base 2. This means that instead of using the ten digits 0–9 that are used in the decimal system (base 10), binary only uses 0 and 1. Binary numbers are used in computing because all information inside a computer is stored as binary digits, or bits. Every letter, number, and character can be represented in binary.
Writing Binary Numbers
Before you can start converting a fractional decimal number to binary, you need to understand how to write binary numbers. In the binary system, positions to the left of the last digit represent increasing powers of two from right to left. For example, the number 101 is equal to 1 × 22 + 0 × 21 + 1 × 20, which is equal to 4 + 0 + 1, or 5.
How to Convert a Fractional Decimal Number to Binary
Now that you understand how binary numbers work, you can start converting a fractional decimal number like 6.75 to binary. This can be done with a two-step process. First, convert the whole number part of the number to binary, then convert the fractional part to binary.
Step 1: Convert the Whole Number Part
To convert the whole number part of 6.75, you can use the same process as you used to convert the number 101 above. Start with 6 and divide it by 2. The remainder is 0, so write down a 0. Then, divide 6 by 2 again. The remainder is 0, so write down another 0. Continue dividing 6 by 2 until you get a result that’s less than 1. The result should be 0.75. Once you get here, note down the last remainder, which should be 1.
The binary number for 6 is 110. This means that 6.75 in binary is 110.11.
Step 2: Convert the Fractional Part
To convert the fractional part of 6.75 to binary, start by multiplying 0.75 by 2. The result should be 1.50. Write down the 1 and carry the 0.50 over to the next step. Then, multiply 0.50 by 2. The result should be 1.00. Again, note down the 1 and carry the 0.00 over to the next step. Repeat this process until you either get a result of 1 or the sequence starts to repeat.
In this case, the result should be
