# 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 16

= 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 8

= 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 2

= 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 16

= 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

 Decimal Binary Octal Hexadecimal 0000 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

BASIC COMPUTER CONCEPT

APPLICATION SOFTWARE

ART OF INFORMATION PROCESSING

COMPUTER HARDWARE

DATA AND INFORMATION

SUBSCRIBE BELOW FOR A GIVEAWAY

Building & maintaining an elearning portal is very expensive, that is why you see other elearning websites charge fees. Help to keep this learning portal free by telling mum or dad to donate or support us. We accept grants, sponsorships & support to help take this to the next big level and reach out to more people. Thank you so much. Click here to donate

error: Content is protected !!