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# 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. 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

 Decimal Binary Octal Hexadecimal 0 0000 0 0 1 0001 1 1 2 0010 2 2 3 0011 3 3 4 0100 4 4 5 0101 5 5 6 0110 6 6 7 0111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F

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

Website Developer | Certified Microsoft Innovative Educator (MIE)| Certified Google Digital Marketing Expert| A Lecturer| An Author.

#### Author: Samuel Okeke

Website Developer | Certified Microsoft Innovative Educator (MIE)| Certified Google Digital Marketing Expert| A Lecturer| An Author.