Transcription of NUMBER SYSTEMS AND CODES - fu-berlin.de
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NUMBER SYSTEMS AND CODES - fu-berlin.de
1 NUMBER SYSTEMSAND CODESA rithmetic operations using decimal numbers are quite common. However, in logicaldesign it is necessary to perform manipulations in the so-called binary system of num-bers because of the on-off nature of the physical devices used. The present chapter isintended to acquaint the reader with the fundamental concepts involved in dealing withnumber SYSTEMS other than decimal. In particular, the binary system is covered in con-siderable POSITIONAL NOTATIONAn ordinary decimal NUMBER can be regarded as a polynomial in powers of 10. For ex-ample, can be regarded as 4 102 + 2 101 + 3 100 + 1 10 1 + 2 10 numbers like this are said to be expressed in a NUMBER system with base, orradix, 10 because there are 10 basic digits (0, 1, 2.)
(c) (410) 10 = (3120) 5 5 410 (Remainder) 5 82 0 5 16 2 5 3 1 0 3 Now consider the portion of the number to the right of the decimal point, i.e., the fractional part. The procedure for converting this is to multiply (N )10 (fractional) by b. If the resulting product is less than 1, then the most significant (leftmost) digit of the
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