How do you determine the binary equivalent of a decimal fraction?

To determine the binary equivalent of a decimal fraction, you multiply the fraction by 2 and record the integer part.

In more detail, the process of converting a decimal fraction into binary involves a series of multiplications by 2. This is also known as the 'double and record' method. Here's how it works:

First, you multiply the decimal fraction by 2. The integer part of the result (either a 0 or a 1) is the first digit (after the binary point) of the binary equivalent. The fractional part of the result is used for the next calculation.

You then repeat this process: multiply the fractional part by 2 and record the integer part. This gives you the next digit of the binary equivalent. You continue this process until you've achieved the desired level of precision or until the fractional part becomes zero.

For example, let's convert the decimal fraction 0.375 into binary.

1. Multiply 0.375 by 2 to get 0.75. The integer part is 0 and the fractional part is .75.
2. Multiply .75 by 2 to get 1.5. The integer part is 1 and the fractional part is .5.
3. Multiply .5 by 2 to get 1.0. The integer part is 1 and the fractional part is 0.

So, the binary equivalent of 0.375 is .011.

It's important to note that not all decimal fractions can be precisely represented in binary. For example, the decimal fraction 0.1 cannot be exactly represented in binary. In such cases, the binary equivalent will be an approximation.

Also, remember that this method is for converting decimal fractions, not whole numbers. The process for converting whole numbers is different and involves division by 2 instead of multiplication.