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CONVERSION OF OTHER BASES TO DENARY SYSTEM

CONVERSION OF OTHER BASES TO DENARY SYSTEM

Conversion of other bases to denary system. To convert numbers in the other bases to denary system, expand the given number in power of its bases.

 

Examples:

  1. Convert 35416 to denary

35416 = 3 x 162 + 5 X 161 + 4 x 160

= 3 x 256 + 5 x 16 + 4 x 1

= 768 + 80 + 4

852ten

  1. Convert 255eight to base ten

2558   = 2 x 82 + 5 x 81 + 5 x 80

= 2 x 64 + 5 x 8 + 5 x 1

= 128 + 40 + 5

= 173ten

  1. Convert 10110012 to base ten

1011001two = 1 x 26 + 0 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20

= 1 x 64 + 0 x 32 + 1 x 16 + 1 x 8 + 0 X 4 + 0 x 2 + 1 x 1

= 64 + 0 + 16 + 8 + 0 + 0 +1

= 89ten

 

  1. Convert 3A716 to base ten

3A716 = 3 x 162 + 10 x 161 + 7 x 160

                = 3 x 256 + 10 x 16 + 7 x 1

= 768 + 160 + 7

= 935ten

 

ADDITION, SUBTRACTION AND MULTIPLICATION OF BINARY NUMBERS

There are four rule guiding binary addition

0 + 0 = 0

0 + 1 = 1   (Always remember you are working with binary digit not decimal)

1 + 0 = 1

1 + 1 = 10

 

  1. Add 1012 + 10002
  2. Add 10011012 + 1110012

 

  1. 1012

+ 10002

11012

 

  1. 10011012

+    1110012

100001102

 

Binary Subtraction

0 – 0 = 0; 0 – 1 = 1; 1 – 0 = 1; 1 – 1 = 0

(1). Subtract 1012 from 10012     (2). 100012 – 11112

  1. 10012

–       1012

1002

 

  1. 10001

–         1111

00102

 

Binary Multiplication

The rules for binary multiplication are: 0 x0 = 0; 1 x 0 = 0; 0 x 1 = 0; 1 x 1 = 1

(1).11012 x 1102                                          (2). 1012 x 102

  1. 11012

x       1102

00002

+     11012

11012

10011102

 

  1. 1012

x     102

0002

+  1012

10102

 

 

DecimalBinaryOctalHexadecimal
0000000
1000111
2001022
3001133
4010044
5010155
6011066
7011177
81000108
91001119
10101012A
11101113B
12110014C
13110115D
14111016E
15111117F

 

EVALUATION

  1. Define number base
  2. Convert the following to base 10
  • 10011two
  • 317eight
  1. Evaluate the following:
  • 1012 x 1012
  • 1110012 + 10012
  • 101112 – 1002

 

See also

BASIC COMPUTER CONCEPT

APPLICATION SOFTWARE

ART OF INFORMATION PROCESSING

COMPUTER HARDWARE

DATA AND INFORMATION

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