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Machine Theory

Fundamentals of Digital Machine Computing by Guenther Hintze (auth.)

By Guenther Hintze (auth.)

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The most commonly used complement notations for negative numbers are the ten's and nine's complement in the decimal number system and the corresponding two's and one's complement in the binary number system. The complements Y' of a number Y are defined in the binary system as follows: Two's complement One's complement (2-6) Y'= 2n+ 1- Y-1 31 BINARY NUMBERS AND CODES where in general n is the number of digits in Y, 2n is the sign digit, and 2n+ 1 the digit position to the left of the sign digit.

INITIAL COMPUTER INPUT The previously described binary numbers and codes are used in that portion of the communication with the computer which is done automatically in the input and output circuits of the computer. The user of the computer will then ask the question what communication means and formats are available to him who ultimately has to define the input before the automatic portion of the computer takes over. For the initial transcription into machine-sensible media, mainly punched cards, punched tape, and recently, writing with magnetic ink are used.

For this reason and in order to avoid in the arithmetic circuitry the inclusion of the logic which implements both, the addition and subtraction tables, machine designers prefer normally to obtain subtraction through the addition of a complement. The most commonly used complement notations for negative numbers are the ten's and nine's complement in the decimal number system and the corresponding two's and one's complement in the binary number system. The complements Y' of a number Y are defined in the binary system as follows: Two's complement One's complement (2-6) Y'= 2n+ 1- Y-1 31 BINARY NUMBERS AND CODES where in general n is the number of digits in Y, 2n is the sign digit, and 2n+ 1 the digit position to the left of the sign digit.

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