Binary Representation Of Numbers Worksheet - Autar Kaw, University Of South Florida Page 10
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1
2
3
4
5
6
7
8
9
10
11
123
1
3
1
0
3
2
1
0
(
11
)
=
2
+
2
+
1
=
2
+
2
+
2
=
1
×
2
+
0
×
2
+
1
×
2
+
1
×
2
=
(
1011
)
10
2
To convert
to the base 2, we proceed as follows. What is the smallest
(
. 0
1875
)
10
negative power of 2 that is less than or equal to 0.1875. That power is
as
−
3
−
3
.
2
=
. 0
125
So
−
3
. 0
1875
=
2
+
. 0
0625
What is the next smallest negative power of 2 that is less than or equal to 0.0625. That
−
4
power is
as
.
−
4
2
=
. 0
0625
So
−
3
−
4
. 0
1875
=
2
+
2
Hence
−
3
−
3
−
4
−
1
−
2
−
3
−
4
(
. 0
1875
)
=
2
+
. 0
0625
=
2
+
2
=
0
×
2
+
0
×
2
+
1
×
2
+
1
×
2
=
(
. 0
0011
)
10
2
Since
(
11
)
=
(
1011
)
10
2
and
(
. 0
1875
)
=
(
. 0
0011
)
10
2
we get
(
11
.
1875
)
=
(
1011
.
0011
)
10
2
Can you show this algebraically for any general number?
Example 2
Convert
to base 2.
(
13
.
875
)
10
Solution
For
, conversion to binary format is shown in Table 4.
(
13
)
10
Source URL:
Saylor URL:
Attributed to: University of South Florida: Holistic Numerical Methods Institute
Page 10 of 12
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