Page 23 - Handout Digital Electronics

Example 2:

Convert 19710 to binary using Binary Exponential Placeholders. The highest Binary Exponential
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Placeholders next to 197 are 128, which is 2 . If 128 can be subtracted from 197, we write a 1 in
column 128, Subtract 128 from 197. The answer is 69. If 64 can be subtracted from 69, we put a 1 in
column in
64. We subtract 64 from 69. The answer is 5. 32 cannot be subtracted from 5. We put a zero (0) in
column 32. Next is column 8, which cannot be subtracted from 5 and we put a 0 in column 8. Next is
column 4. 4 can be subtracted from 5, so we put a 1 in column 4. Subtract 4 from 5 and the answer is 1.
Next column is 2 and 2 cannot be subtracted from 1 and we write a 0 in column 2. Next column is 1 and
1 can be subtracted from 1, so we put a 1 in column 1.

Positional weight 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0
Value 128 64 32 16 8 4 2 1
Number 1 1 0 0 0 1 0 1

So, 1 1 0 0 0 1 0 12 is equivalent to 19710

1.9 Method 3: Using the Multiplication method to convert decimal fractions to binary

Decimal fractions are converted to binary fractions equivalent to using the multiplication

method. Steps

1. Write down the decimal fraction
2. Multiply the decimal fraction by 2
3. Write down the whole number part
4. Repeat steps 2 and 3 until the degree of accuracy has been achieved.
5. Write down the whole numbers in the order you produced them.

Note that when converting decimal fractions to their binary equivalents, we should do this to a given
degree of accuracy, i.e. the number of decimal points places that are needed. When using binary
fractions, it is recommended to use a smaller number of decimal places as the fractions become very
inaccurate as the number of decimal points increases.

Example1:

Convert 0.12510 to binary equivalent

.125 2 0.250 whole number part 0 MSB
.250 2 0.500 whole number part 0
.500 2 1.000 whole number part 1 LSB

Thus, the binary equivalent of 0.12510 is 0012

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