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# Class Note for ECE 380 at UA-Digital Logic(24)

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Alabama - Tuscaloosa taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15
Other number representations ECE380 Digital Logic Number Representation and Arithmetic Circuits Other Number Representations Previously we dealt with binary integers signed or unsigned in a positional number representation 0 Other number representations are also commonly used Fixedpoint allows for fractional representation Floatingpoint allows for high precision very large andor very small numbers Binarycoded decimal BCD another form for integer representation mama a cumma mamau m n i imam Levine 2n 1 mama a comma Ensquotaqua m n i imam Lam 2n 2 Fixedpoint numbers Fixedpoint numbers A xedpoint number consists of integer and fraction parts 0 In positional notation it is written as Bbn1bn2 b1b0b1b2bk With a corresponding value of VB Cbix2i The position of the radix point is assumed to be fixed 0 For example B01001010101012 B 1x261x231x211x211x231x25 B6482512503125 B746562510 B8AA816 Logic circuits that deal with fixed point numbers are essentially the same as those used for integers mama a cumma mamau m n i imam Levine 2n i mama a comma Ensquotaqua m n i imam Lam 2n a Floatingpoint numbers IEEE single precision format o Fixedpoint numbers have a range that is limited by the significant digits used to represent the number 0 For some applications it is often necessary to deal with numbers that are very large or very small 0 For these cases it is better to use a floatingpoint representation in which numbers are represented by a mantissa comprising the significant digits and an exponent of the radix R o The format is Mantissa x R we 0 The numbers are usually normalized such that the radix point is placed to the right of the first nonzero digit for example 5234x1043 or 375x10 35 o The IEEE defines a 32bit single precision format for floating point values Sign bit S most significant bit 8bit exponent field E excess 127 exponent True exponent E7127 E0 rgt 32bltvalue0 E255 rgt 327b t valuew 23bit mantissa M Isl E M l 2 Sign 8bit 0 deno39ies excess127 23quot 1 denotes exponent maquot 39555 new a cunning Enune ng m n J 101am Levine 2n 5 Elainel a calming Enune lm m n J Jclsnn Lain 2n 5 IEEE single precision format Floatingpoint example The IEEE standard calls for a normalized mantissa which means that the most significant bit is always set to 1 o It is not necessary to include this bit explicitly in the mantissa field If M is the value in the 23bit mantissa field the true 24bit mantissa is actually 1M The value of the floating point number is then Value 15M x ZE 127 o For example 0100000001 1000000000000000000000 1112x2lt125 127gt 1112x21 1112 1x211x201x2 13510 What is the following 001 1 1 1 1 101 1000000000000000000000 new a cunning Enune ng m n J 101am Levine 2n 1 Elainel a calming Enune lm m n J Jclsnn Lain 2n n Bina rycodeddecimal numbers ASCII character code o It is possible to represent decimal numbers simply by encoding each decimal digit in binary form Called binarycodeddecimal BCD 0 Because there are 10 digits to represent it is necessary to use four bits per digit From 00000 to 91001 01111000BCD7BJEI o BCD representation was used in some early computers and many handheld calculators Provides a format that is convenient when numerical information is to be displayed on a simple digitoriented display 0 The most popular code for representing information in computers is used for both numbers and letters and some control codes 0 It is the American Standard Code for Information Interchange ASCII code 0 ASCII code uses sevenbit patterns to represent 128 different symbols including Digifs 09 Lowercase az and uppercase AZ characters Punctuation marks and other commonly used symbols Control cods o The 8bit extended ASCII code is used to represent all of the above and another 128 graphics characters Elwtnul a cumnu Enunmng m n J helmquot Levine 2n 9 z lmnul a comma Enunml39 nrnJJclsm Lajllelnm Example ASCII character codes 1000001ASCH41H A 1000010ASCH42H B 1100001ASCH61H a 1100010Ascn62H b 0110000ASCH30H 0 0111001ASCH39H 9 ASCII table given in the textbook Elwtnul a cumnu Enunmng m n J helmquot Levine 2n 11

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