Merlin's
Blue*
Fact
Sheets

Number Systems

   
 

Feel free to
print this page
for future reference.

Tables showing and explaining number systems including:
decimal, binary, octal and hexadecimal equivalents.

 
0 to 21 (decimal) and their equivalents

Decimal

Binary

Octal

Hex

0

00000

0

00

1

00001

1

01

2

00010

2

02

3

00011

3

03

4

00100

4

04

5

00101

5

05

6

00110

6

06

7

00111

7

07

8

01000

10

08

9

01001

11

09

10

01010

12

0A

Decimal

Binary

Octal

Hex

11

01011

13

0B

12

01100

14

0C

13

01101

15

0D

14

01110

16

0E

15

01111

17

0F

16

10000

20

10

17

10001

21

11

18

10010

22

12

19

10011

23

13

20

10100

24

14

21

10101

25

15


Some key numbers and their equivalents

Some key values in the range of (decimal) 30 to 100. Note the binary equivalents of 32 and 64.

Decimal

Binary

Octal

Hex

30

11110

36

1E

32

100000

40

20

40

101000

50

28

50

110010

62

32

60

111100

74

3C

64

1000000

100

40

Decimal

Binary

Octal

Hex

70

1000110

106

46

80

1010000

120

50

90

1011010

132

5A

100

1100100

144

64

Why do we have different number systems?
Computer systems store all information in binary form (combinations of ones and zeroes). There are places in some systems where information is handled or processed in hexadecimal or octal form. Some people need to be able to readily convert values from one form to another. Some computer systems provide a ready-reckoner calculator to help do this (eg. MS Windows' Calculator - Start, Programs, Accessories). The sample conversion tables above, and number system explanations below, will help to shed some light on this topic.

Decimal Number System
In the decimal number system (the number system with which most of us are very familiar, and also known as "base 10"), each digit in a five digit number has a placeholder value and meaning as shown here:-
  eg. In the decimal number   57,362:- placeholder
value
 

the digit 5 means
the digit 7 means
the digit 3 means
the digit 6 means
the digit 2 means

50,000
7,000
300
60
2

  (the number of 10,000s)
(the number of thousands)
(the number of hundreds)
(the number of tens)
(the number of units)
  and when added up, the sum of these five decimal numbers is: 57,362
Binary Number System
In the binary number system (referred to as "base 2") the digit places in a seven digit binary number are as explained in the following example.
  eg. In the 7-digit binary number 1011010 (the binary equivalent for decimal 90), each digit (from left to right) has a placeholder value and meaning as shown here:-
 

placeholder
value

 

decimal
equivalent

  explanation
 

the first 1 represents
the first 0 represents
the next 1 represents
the next 1 represents
the next 0 represents
the next 1 represents
the next 0 represents

64
32
16
8
4
2
1

 

64
0
16
8
0
2
0

  there is one value = 64
there are NO values = 32
there is one value = 16
there is one value = 8
there are NO values = 4
there is one value = 2
there are NO values = 1
  and when the decimal equivalent values are added up, the sum is: (decimal) 90
Hexadecimal Number System
In the hexadecimal number system (or just "hex" for short, and known as "base 16") the digit places in a hexadecimal number are as explained in the following example. You might notice that a large decimal number (with several digits) is represented in hex with fewer digits.
  eg. The hex equivalent of decimal 60 = 3C. In this hex number the two digits (from left to right) have placeholder values and meaning as shown here:-
 

placeholder
value

 

decimal
equivalent

  explanation
 

the digit 3 represents
the "digit" C represents

16
(units)

 

48
12

  there 3 lots of 16
in hex, C = decimal 12
  and when the decimal equivalent values are added up, the sum is: (decimal) 60
Octal Number System
In the octal number system (known as "base 8") the digit places in an octal number are as explained in the following example.
  eg. The octal equivalent of decimal 90 = 132. In this octal number the three digits 132 (from left to right) have placeholder values and meaning as shown here:-
 

placeholder
value

 

decimal
equivalent

  explanation
 

the digit 1 represents
the digit 3 represents
the digit 2 represents

64
8
1

 

64
24
2

  there is 1 value = 64
there are 3 values = 8
there are 2 values = 1
  and when the decimal equivalent values are added up, the sum is: (decimal) 90


* - Merlin's Blue Fact Sheets are so named because the first versions (produced in 1989) were printed onto blue paper to help them stand out in a pile of plain paper. And today on the Web, the page background is blue.

Printing this page

Computer Glossary

Searching this site

Searching the Web

Please feel free to print this web page, and/or pass it on to others, provided that it is printed in entirety including the Copyright notice and home page web address below. Some of the computer terms used here are explained in our on-line Glossary of (Computer) Terms (it will open in a new Window). For a more complete glossary have a look at our Merlin's Techno-Guide. To search this web site for specific information, you can use the PicoSearch facility on our home page. Or to search the Web using a search engine, try browsing a Search Engine, Directory, Portal Web site from our (extensive list) Search Engines page, or the abridged version of the same page.


Home |  Merlins Techno-Guide |  On-line Glossary | Search this site | Back to Top | Help Index Page

This site built and maintained by Robert B. Brain (in his spare time).
Please feel free to send feedback and suggestions by email.
Email to: brain at the domain: hotkey.net.au
(Sorry, but this email address is coded to elude spammers).

© Copyright 1999-2003, Colonial Pioneer Publishing (ABN: 52 791 744 975).
http://www.hotkey.net.au/~brain
Last revised: 20 May, 2003.


Important: The information provided here is not advice. It is intended as a guide only, and may not be complete, nor relevant to every situation. It should not be relied upon. Any product or company names that might be mentioned here may be registered trade marks or trade names and owned by the respective companies, and they are are quoted here in good faith, without recommendation or endorsement.