Merlin's Blue* Fact Sheets 

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Tables showing and explaining number systems including: 


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 readyreckoner 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 the digit 5 means 50,000 placeholder decimal the first 1 represents 64 64 placeholder decimal the digit 3 represents 16 48 placeholder decimal the digit 1 represents 64 64
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:
Binary Number System
eg. In the decimal number 57,362:
placeholder
value
the digit 7 means
the digit 3 means
the digit 6 means
the digit 2 means
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
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.
Hexadecimal Number System
eg. In the 7digit binary number 1011010 (the binary equivalent for decimal 90), each digit (from
left to right) has a placeholder value and meaning as shown here:
value
equivalent
explanation
the first 0 represents
the next 1 represents
the next 1 represents
the next 0 represents
the next 1 represents
the next 0 represents
32
16
8
4
2
1
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
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.
Octal Number System
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:
value
equivalent
explanation
the "digit" C represents
(units)
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
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:
value
equivalent
explanation
the digit 3 represents
the digit 2 represents
8
1
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
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