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

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Last revised: 20 May, 2003.