Binary And Hexadecimal Numeration And Logical Operations Worksheet - Object Oriented Programming In Java, Marian Manyo Page 2
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12J A V A
L A B
M A N U A L
1.1 BINARY NUMERATION – WHOLE NUMBERS
In both class and the text book, you have seen that binary numerals use the digits 0 and 1 and are based
on grouping in groups of two. A place value diagram for a binary numeral using eight digits is
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128
64
32
16
8
4
2
1
2
2
2
2
2
2
2
2
7
6
5
4
3
2
1
0
high bit
low bit
E x e r c i s e 1 . 1 Count from 0 to 15 in binary, record the binary numerals
decimal
binary
decimal
binary
0
8
1
9
2
10
3
11
4
12
5
13
6
14
7
15
Binary to Decimal:
Given a binary numeral, to find the decimal numeral, add the place values that contain a one.
1101 =
= 8 + 4 + 1 = 13
1
1
0
1
8
4
2
1
11000011 =
1
1
0
0
0
0
1
1
= 128 + 64 + 2 + 1 = 195
128
64
32
16
8
4
2
1
Decimal to Binary:
Given a decimal numeral, to determine the binary numeral, place a one in the place values that sum to
the number, fill in the remaining places with a zero.
9 =
= 8 + 1
1001
1
1
0
1
8
4
2
1
1
0
0
0
1
1
0
0
140 =
= 128 + 8 + 4
10001100
128
64
32
16
8
4
2
1
P A G E 1 . 2
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
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