Binary And Hexadecimal Numeration And Logical Operations Worksheet - Object Oriented Programming In Java, Marian Manyo Page 5
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12J A V A
L A B
M A N U A L
B. Convert the decimal numeral 51 to binary
1.2 BINARY FRACTIONS
In the decimal numeration system, the whole portion of a number is separated from the fractional portion
with a decimal point. To the right of the point, the place values continue the pattern established to the left
of the decimal point.
____
____
____
.
____
____
____
____
100
10
1
1/10
1/100
1/1000
1/10000
10
10
10
10
10
10
10
2
1
0
-1
-2
-3
-4
Similarly, in the binary numeration system, the whole portion of a number is separated from the fractional
portion with a binary point.
____
____
____
.
____
____
____
____
4
2
1
1/2
1/4
1/8
1/16
2
2
2
2
2
2
2
2
1
0
-1
-2
-3
-4
Binary fraction to decimal fraction
This process is the same that is used with whole numbers.
represents
or
0.1011
1/2 + 1/8 + 1/16 = 11/16
0.6875
2
represents
or
101.101
4 + 1 + 1/2 + 1/8 = 5 5/8
5.625
2
E x e r c i s e 1 . 5 Complete the chart, converting the binary numerals to decimal numerals.
binary
decimal
0.111
10.01
1011.1001
M A R I A N M A N Y O , M A R Q U E T T E U N I V E R S I T Y
P A G E 1 . 5
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