1-63The BINARY NUMBER SYSTEM is a base 2 system. The symbols 1 and 0 can be used torepresent the state of electrical/electronic devices. A binary 1 may indicate the device is active; a 0 mayindicate the device is inactive.The OCTAL NUMBER SYSTEM is a base 8 system and is quite useful as a tool in the conversionof binary numbers. This system works because 8 is an integral power of 2; that is, 2^{3} = 8. The use of octalnumbers 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. Abinary number can be converted directly to a base 16 number if the binary number is first broken intogroups of four digits.The basic rules of ADDITION apply to each of the number systems. Each system becomes uniquewhen carries are produced.SUBTRACTIONin each system is based on certain rules of that number system. The borrow variesin magnitude according to the number system in use. In most computers, subtraction is accomplished byusing 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 bythe base of the number system to which you are converting. Continue dividing the quotient of theprevious division until it can no longer be done. Extract the remaindersthe remainder from the firstcomputation will yield the LSD; the last will provide the MSD.

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