Binary Representation Of Numbers Worksheet - Autar Kaw, University Of South Florida Page 6
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1
2
3
4
5
6
7
8
9
10
11
12Hence
(
. 0
1875
)
=
(
a
a
a
a
)
10
−
1
−
2
−
3
−
4
2
=
(
. 0
0011
)
2
The algorithm for any fraction is given in a flowchart on the next page.
Having calculated
(
11
)
=
(
1011
)
10
2
and
,
(
. 0
1875
)
=
(
. 0
0011
)
10
2
we have
.
(
11
.
1875
)
=
(
1011
.
0011
)
10
2
In the above example, when we were converting the fractional part of the number, we
were left with 0 after the decimal number and used that as a place to stop. In many
cases, we are never left with a 0 after the decimal number. For example, finding the
binary equivalent of 0.3 is summarized in Table 3.
Table 3. Converting a base-10 fraction to approximate binary representation.
Number after
Number before
Number
decimal
decimal
0
= a
0.3 × 2
0.6
0.6
−
1
1
= a
0.6 × 2
1.2
0.2
−
2
0
= a
0.2 × 2
0.4
0.4
−
3
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Attributed to: University of South Florida: Holistic Numerical Methods Institute
Page 6 of 12
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