e. The last objective to learn in this text is to convert fractions expressed in decimals and their
binary equivalent from one base to the other. Base 10 fractions can be expressed by numbers with a
decimal point, for example, 3/4 is the same as 0.75. similarly, base 2 fractions can be expressed in
numbers following a binary point, for example, 1/102 is the same as 0.12.
In the base 10 system, numbers to the left of the decimal point are whole numbers, and numbers to the
right of the decimal point are fractions. The same thing is true in the binary system, or for that matter for
any other number base.
Look at the binary numbers to the left of the binary point first (Figure 1-7):
Figure 1-7
Starting from the right side of the chart, the base 10 value of each binary digit is shown. A binary 1 in the
righth and position next to the binary point will have a base 10 value of 1. A binary 1 in the next position
has a base 10 value of 2. A binary 1 in the third position from the right has a base 10 value of 4, and each
successive digit doubles in value.
Another way to calculate the base 10 value of a binary number is to add up the base 10 value of each of
its digits. The binary number 1111111 has a base 10 value of 64 + 32 + 16 + 8 + 4 + 2 + 1 or 12710.
Since each value to the left has a value twice the preceding one, then each value to the right has a value of
half the preceding one. This relationship continues to the right of the binary point, too. Thus, the first
value to the right of the binary point is 1/2, the next 1/4, and so on. This is shown on the chart in figure 1-
8 below:
Figure 1-8
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