数字设计基础双语课件(第1章).ppt
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1、 1.Digital systems&representation 1.1 Digital systems 1.2 Numbers representation1.3 Performing arithmetic with binary numbers1.4 Representation of alphanumeric symbols1 1.1 Digital Systems1.The realm of digital systemsA digital system is often designed to satisfy two kinds of tasks:(1)To control app
2、aratus(2)To perform calculationsA digital system can perform some calculations and on the basis of the result,take certain control actions.2 1.1 Digital Systems2.Two-valued logic signals The input and output signals have only two values.Hence,the digital systems might use 5 volts and 0 volts to repr
3、esent the two values.3.Positive and negative logic representation(1)Positive logic representationThe higher voltage represents a logic 1,and the lower voltage represents a logic 0.3 1.1 Digital Systems(2)Negative logic representationThe higher voltage represents a logic 0,and the lower voltage repre
4、sents a logic 1.(3)Mixed logic representationUsing both positive and negative representations in the same system.4 1.1 Digital Systems4.Logic functionsIn order to develop the algorithm or logic function for a digital system,logic signals must be represented by names as in algebra.Logic function can
5、be written in a two-valued algebra called Boolean algebra.5.Three fundamental logic operationsAND,OR,and NOT are three fundamental logic operations,from which any complicated logic function can be created.5 1.2 Numbers Representation1.Decimal numbersDecimal number system has ten digits 0,1,2,3,4,5,6
6、,7,8 and 9.It is a positional number system,which uses digits multiplied by powers of 10 that depend upon the position of the digit.10 is the base of the number system.(235)10=2102+3101+5100Ten different voltages are needed for each possible value of the digit in the decimal number system.Then elect
7、ronic circuits will have to be designed which can accept ten different voltages and produce ten different voltages,one for each digit of the number.6 1.2 Numbers Representation2.Binary numbersBinary number system has only two digits 0 and 1.They are called bits(binary digits).2 is the base of the bi
8、nary system.Binary number can be represented as:(110001)2=125+124+023+022+021+120Numbers can be a fraction or have a fractional part.(0.101)2=12-1+02-2+12-3The binary number system fits in well with digital systems.There are only two digits used,0 and 1,in all numbers,so only two different voltages
9、are needed for each digit.7 1.2 Numbers Representation3.Hexadecimal and octal numbersThe positional number system using the base of 16 is called the hexadecimal number system.The 16 different numbers are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F.The positional number system using the base of 8 is called t
10、he octal number system.The 8 different numbers are 0,1,2,3,4,5,6 and 7.8 1.2 Numbers Representation4.Number conversionNumbers are likely to be entered using the decimal representation,but dealt in binary within the digital systems.Therefore,there needs to be some way of converting from binary to dec
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