Java Reference
In-Depth Information
F.2 Conversions Between Binary and Decimal Numbers
Given a binary number
b
n
b
n
-
1
b
n
-
2
c
b
2
b
1
b
0
, the equivalent decimal value is
binary to decimal
2
n
2
n
-
1
2
n
-
2
2
2
2
1
2
0
b
n
*
+
b
n
-
1
*
+
b
n
-
2
*
+ c +
b
2
*
+
b
1
*
+
b
0
*
Here are some examples of converting binary numbers to decimals:
Binary
Conversion Formula
Decimal
10
2
2
1
2
0
1
*
+
0
*
1000
8
2
3
2
2
2
1
2
0
1
*
+
0
*
+
0
*
+
0
*
10101011
171
2
7
2
6
2
5
2
4
2
3
2
2
1
*
+
0
*
+
1
*
+
0
*
+
1
*
+
0
*
+
2
1
2
0
1
*
+
1
*
To convert a decimal number
d
to a binary number is to find the bits
b
n
,
b
n
—
1
,
b
n
—
2
, . . . ,
b
2
,
b
1
and
b
0
such that
decimal to binary
2
n
-
1
2
n
-
2
2
n
2
2
2
1
2
0
d
=
b
n
*
+
b
n
-
1
*
+
b
n
-
2
*
+ c +
b
2
*
+
b
1
*
+
b
0
*
These bits can be found by successively dividing
d
by 2 until the quotient is 0. The remainders
are
b
0
,
b
1
,
b
2
,
c
,
b
n
-
2
,
b
n
-
1
, and
b
n
.
For example, the decimal number 123 is 1111011 in binary. The conversion is done as follows:
Quotient
0
1
3
7
15
30
61
21
0
1
23
2
27
6
2
15
14
2
30
2
61
2
123
30
60
122
1
Remainder
1
1
1
0
1
b
6
b
5
b
4
b
3
b
2
b
1
b
0
Tip
The Windows Calculator, as shown in Figure F.1, is a useful tool for performing number
conversions. To run it, search for
Calculator
from the
Start
button and launch Calcula-
tor, then under
View
select
Scientific.
Decimal
Binary
Hex
F
IGURE
F.1
You can perform number conversions using the Windows Calculator.
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