Binary Representation Of Numbers Worksheet - Autar Kaw, University Of South Florida Page 3
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12Table 1 Converting a base-10 integer to binary representation.
Quotient
Remainder
1 a
=
11/2
5
0
1 a
=
5/2
2
1
0 a
=
2/2
1
2
1 a
=
1/2
0
3
Hence
(
11
)
=
(
a
a
a
a
)
10
3
2
1
0
2
=
(
1011
)
2
For any integer, the algorithm for finding the binary equivalent is given in the flow chart
on the next page.
Now let us look at the decimal part, that is, 0.1875.
1. Multiply 0.1875 by 2. This gives 0.375. The number before the decimal is 0 and
the number after the decimal is 0.375. Since the number before the decimal is 0,
.
a
=
0
−
1
2. Multiply the number after the decimal, that is, 0.375 by 2. This gives 0.75. The
number before the decimal is 0 and the number after the decimal is 0.75. Since
the number before the decimal is 0,
.
a
=
0
−
2
3. Multiply the number after the decimal, that is, 0.75 by 2. This gives 1.5. The
number before the decimal is 1 and the number after the decimal is 0.5. Since
the number before the decimal is 1,
.
a
=
1
−
3
4. Multiply the number after the decimal, that is, 0.5 by 2. This gives 1.0. The
number before the decimal is 1 and the number after the decimal is 0. Since the
number before the decimal is 1,
a
=
1
.
−
4
Since the number after the decimal is 0, the conversion is complete. The above steps
are summarized in Table 2.
Table 2. Converting a base-10 fraction to binary representation.
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Attributed to: University of South Florida: Holistic Numerical Methods Institute
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