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The BINARY NUMBER SYSTEM is a base 2 system. The symbols 1 and 0 can be used to
represent the state of electrical/electronic devices. A binary 1 may indicate the device is active; a 0 may
indicate the device is inactive.
The OCTAL NUMBER SYSTEM is a base 8 system and is quite useful as a tool in the conversion
of binary numbers. This system works because 8 is an integral power of 2; that is, 23 = 8. The use of octal
numbers reduces the number of digits required to represent the binary equivalent of a decimal number.
The HEX NUMBER SYSTEM is a base 16 system and is sometimes used in computer systems. A
binary number can be converted directly to a base 16 number if the binary number is first broken into
groups of four digits.
The basic rules of ADDITION apply to each of the number systems. Each system becomes unique
when carries are produced.
SUBTRACTION in each system is based on certain rules of that number system. The borrow varies
in magnitude according to the number system in use. In most computers, subtraction is accomplished by
using the complement (R’s or R’s-1) of the subtrahend and adding it to the minuend.
To CONVERT A WHOLE BASE 10 NUMBER to another system, divide the decimal number by
the base of the number system to which you are converting. Continue dividing the quotient of the
previous division until it can no longer be done. Extract the remainders the remainder from the first
computation will yield the LSD; the last will provide the MSD.
