Binary Representation Of Numbers Worksheet - Autar Kaw, University Of South Florida Page 9
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1
2
3
4
5
6
7
8
9
10
11
12n
n
−
1
0
x
=
a
2
+
a
2
+
. . .
+
a
2
n
n
−
1
0
If we can now find
in the above equation then
a
,.
., .
a
0
n
(
x
)
=
(
a
a
.
. .
a
)
10
n
n
−
1
0
2
We now want to find the binary equivalent of y . So we can write
−
1
−
2
−
m
y
=
b
2
+
b
2
+
. . .
+
b
2
−
1
−
2
−
m
If we can now find
in the above equation then
b
,.
., .
b
−
1
−
m
(
y
)
=
(
b
b
.
. .
b
)
10
−
1
−
2
−
m
2
Let us look at this using the same example as before.
Example 1
Convert
to base 2.
(
11
.
1875
)
10
Solution
To convert
to base 2, what is the highest power of 2 that is part of 11. That power
(
11
)
10
3
is 3, as
to give
2
=
8
3
11
=
2
+
3
1
What is the highest power of 2 that is part of 3. That power is 1, as
to give
2
=
2
1
3
=
2
+
1
So
3
3
1
11
=
2
+
3
=
2
+
2
+
1
0
What is the highest power of 2 that is part of 1. That power is 0, as
= to give
2
1
0
1 =
2
Hence
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Attributed to: University of South Florida: Holistic Numerical Methods Institute
Page 9 of 12
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