Introduction Conversions

3. Number system is used to represent information in quantitative(determinable) form.
TYPES OF NUMBER SYSTEM:
Number system is further divided into following parts:
 DECIMAL NUMBER SYSTEM
 BINARY NUMBER SYSTEM
 OCTAL NUMBER SYSTEM
 HEXADECIMAL NUMBER SYSTEM

4.  Decimal number system has ten-digits represented by (0-9).
 Any decimal number can be represented by these digits and since there are 10 digits
,therefore the base of this number system is 10.

5.  In Binary Number system, we have two digits (0 and 1) .
 Computer represents all kinds of data and information in binary number it includes
audio, graphic etc.
 The base of binary number system is 2.

6.  An Octal Number System has eight digits represented as (0-7) i.e. digits
0,1,2,3,4,5,6.
 The base of octal number system is 8.

7.  The Hexa-Decimal System has 16 digits, which are represented as
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
 The base of hexadecimal number system is 16.

9.  Decimal to Binary Number System
E.g.
(42)10
2 42
2 21-0
2 10-1
2 5-0
2 2-1
2 1-0
(42)10 = (101010)2
 Decimal to Octal Number System
E.g.
(952)10
8 952
8 119-0
8 14-7
8 1-6
8 0-1
(952)10 =(1670)8

10.  Decimal into Hexa –Decimal
E.g.
(428)10
16 428
16 26-12
16 1-10
0-1
(428)10 = (1AC)16

11.  Binary Into Decimal Number System
E.g.
(11001)2
11001=1x24+1x23+0x22+0x21+1x20
=1x16+1x8+0x4+0x2+1x1
=16+8+0+0+1
=25
=(25)10
 Octal Into Decimal Number System
E.g.
(211)8
211=2x82+1x81+1x80
=2x16+1x8+1x1
=128+8+1
=137
=(137)10

12.  Hexa-decimal Into Decimal Number System
E.g.
(DF)16
DF = 13x161+15x160
=13x16+15x1
=208+15
=223
=(223)10

14. Converting from base other than ‘10’ to another base other than ‘10’:
Following are the steps for base conversions:
 Convert the original number to base (10) decimal.
 Convert the decimal number to required base number.

15. Example No.01:
(545)6=?4
STEP-1
545 6
5x6 + 4x6 + 5x6
5x36 +4x6 + 5x1
180 + 24 + 5
=(209)10
STEP-2
4 209
4 52-1
4 13-0
4 3 -1
0 -3
(545)6 = (3101)4

16. Example No.02:
(11010011)2 = ?16
STEP-1:
=1x2+1x2+0x2+1x2+0x2+0x2+1x2+1
x2
=1x128+1x64+0x32+1x16+0x8+0x4+
1x2+1x1
=128+64+0+16+8+4+2+1
=(211)10
STEP-2:
16 211
16 13-3
0-13
(11010011)2 = (D3)16

18. BINARY TO DECIMAL
PROCESS:
 In order to convert binary number system into decimal number system we should
follow following steps:-
 Multiply each bit of the Binary Number by it corresponding bit-weighting factor (i.e.
Bit-0→2=1; Bit-1→21=2; Bit-2→22=4; etc.).
Sum up all the products to get the Decimal Number.

20. ∴ 01102 = 6 10
•EXAMPLE:1
Convert binary number 01102 into decimal
equivalent?

21. •EXAMPLE:2
Convert binary number 01101012 into decimal
equivalent.

22. PROCESS:
 In order to convert binary number system octal number system we should follow
following steps:-
 Take the binary number and from right to left, group all place holders in triplets. Add
leading zeros , if necessary
100011001010012
010 001 100 101 001

24. • Convert each triplet to its single-digit octal equivalent.
010 001 100 101 0012 =
010 001 100 101 001
2 1 4 5 1

25.  Sometimes, it is necessary to use a numbering system that has more than ten base
digits.
 One such numbering system, hexadecimal, is useful on the Web.
 Hexadecimal number, a Base-16 numbering system, is used in specifying web
colors.

27. There are new symbols for the base-16 equivalent of
the base-10 number 10,11,12,14 and 15.