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The Binary Number System:
It is a code that uses only two symbols.
The symbols are 0 &1
This binary symbols are called binary digits.
It is used only 2 digits so that it is called base –
2 number system.
A binary digit is also called a Bit(Binary Digit).
The highest value symbol in the binary number
system is 1.
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept. of CA, CCW, Trichy.
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We can form combinations of bits 0 &1 to represent
numbers greater than 1.
Like that decimal combinations. 0,1,2,3,4,5,6,7,8,9 then
combined these numbers to form the numbers greater
than 9.
0
1
2
3 …….9 likewise.
10
12 13 …….19
0
1
2
3 …….9 likewise.
20
21 23 …….29
After reaching 99 two digit combinations are exhausted.
We use three digit combinations 100,101,102 etc.
The combination of binary number system
0
1 = 10, 11,100
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept. of CA, CCW, Trichy.
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Binary equivalents of decimal numbers from 0 to 15
DECIMAL
BINARY
0
0
1
1
2
10
3
11
4
100
5
101
6
110
7
111
8
1000
9
1001
10
1010
11
1011
12
1100
13
1101
14
1110
15
1111
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept. of CA, CCW, Trichy.
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Base or Radix:
 The binary number system is a base-2
system. It uses only 2 symbols (0 & 1).
 A Base or Radix of a number system refers to
the number of basic symbols used.
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Number
systems
No. of symbols
Binary
2 – (0 &1)
2
Decimal
10 – (0 to 9)
10
Octal
8 – (0 to 7)
8
Hexadecimal
16 – (0 to 9 & A/a to F/f)
16
A – 10, B- 11, C-12, D – 13, E-14 & F- 15
Base / Radix
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept. of CA, CCW, Trichy.
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Conversions:
12 conversions are there. They are
 Binary to Decimal
 Binary to octal
 Binary to Hexadecimal
 Decimal to Binary
 Decimal to Octal
 Decimal to Hexadecimal
 Octal to Binary
 Octal to Decimal
 Octal to Hexadecimal
 Hexadecimal to Binary
 Hexadecimal to Decimal
 Hexadecimal to Octal
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept. of CA, CCW, Trichy.
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In a decimal numbers each digit position has a
weight. Position is considered as right to left.
Position
Weight
1st
1
2nd
2
3rd
4
4th
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8 and so on
For Example,
64
32
16
8
4
2
1
0.0625
0.125
26
25
24
23
22
21
20
2-4
2-3
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept. of CA, CCW, Trichy.
0.25
0.5
2-2
2-1
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1. (100)2 =(?) 10
1
0
0
20 X 0 = 1X0 = 0
21 X 0 = 2X0 = 0
22 X 1 = 4X1 = 4
4
(100)2 =(4) 10
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept. of CA, CCW, Trichy.
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2. (0.1001)2=(?)10
0.1 0
0
1
2 -4 X 1 = 0.0625
2 -3 X 0 = 0
2 -2 X 0 = 0
2 -1 X 1 = 0.5
20 X0=0
0.5625
Ms.V.Yasodha M.C.A.,M.Phil.,SET.,Dept of CA,CCW,Trichy.
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