06 - 31-Aug-102:23 PM Math EEL 3701 EEL 3701 Menu Review of...

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31-Aug-10—2:23 PM Math 1 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo EEL 3701 EEL 3701 Menu • Review of number systems >Binary math >Signed number systems Look into my . .. 1 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo EEL 3701 EEL 3701 Our decimal ( base 10 or radix 10) number system is positional. Review of Number Systems Ex: 9437 10 = 9x10 3 + 4x10 2 + 3x10 1 + 7x10 0 We have a total of (R=10) digits, i.e., {0,1,2,3,4,5,6,7,8,9}; where R = radix Similarly for R=2, 8, 16; R=2 1 is called Binary ; R=2 3 is called Octal ; R=2 4 is called Hexadecimal (or Hex ) 2 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo Thus, for example, 123 10 = 1x10 2 + 2x10 1 + 3x10 0 123 8 = 1x8 2 + 2x8 1 + 3x8 0 or 123 8 = 83 10 123 16 = 1x16 2 + 2x16 1 + 3x16 0 or 123 16 = 291 10
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31-Aug-10—2:23 PM Math 2 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo EEL 3701 EEL 3701 Fractions are also represented positionally as weighted negative powers of the radix or base. Review of Number Systems Ex: 0.125 10 = 0x10 0 + 1x10 -1 + 2x10 -2 + 5x10 -3 Thus, for example, 0.125 8 = 0x8 0 + 1x8 -1 + 2x8 -2 + 5x8 -3 0.125 16 = 0x16 0 + 1x16 -1 + 2x16 -2 + 5x16 -3 In general, if R>1, any rational number N can be represented in a power series given by: 3 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo N = (d 4 , d 3 , d 2 , d 1 , d 0 , d -1 , d -2 , d -3 ) R N=d 4 xR 4 + d 3 xR 3 + d 2 xR 2 + d 1 xR 1 +d 0 + d -1 xR -1 + d -2 xR -2 + d -3 xR -3 m = # of digits in the integer part - 1 k =# of digits in the fractional part m -k = i i R i d = N EEL 3701 EEL 3701 953.78 10 = (d 2 , d 1 , d 0 , d -1 , d -2 ) 10 R=10; m=2; k=2 Decimal Numbers 953.78 10 = 9x10 2 + 5x10 1 + 3x10 0 + 7x10 -1 + 8x10 -2 d i = (9,5,3,7,8) What are: 953.78 10 = _____ 2 953.78 10 = _____ 8 953.78 10 = _____ 16 We’ll get to this later. 4 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo For R > 10 we need additional symbols, e.g., for R=16 we need 6 additional symbols 0,1,2,3,4,5,6,7,8,9 and A,B,C,D,E,F for 10-15 An 7-segment display LED can represent all 16 symbols.
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31-Aug-10—2:23 PM Math 3 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo EEL 3701 EEL 3701 7-Segment LED a b b • Show 7-segment LED in LogicWorks “7 Segment c h c a d e g LogicWorks, 7-Segment Display *” • See also the LogicWorks 4-output device called “Hex Keyboard” • See also the LogicWorks 4-input device called 5 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo abc defg A = 111 1101 GND f abc defg F = ___ ____ 011 1001 “Hex Display” h EEL 3701 EEL 3701 Example: Let N=50 and R=2. We can use R=2 symbols, i.e., {0,1}. How many bits? 50 10 = (d 5 , d 4 , d 3 , d 2 , d 1 , d 0 ) 2 Why? 2 5 =32 and 2 6 =64 and 32 50 64 50 10 = d 5 2 5 + d 4 2 4 + d 3 2 3 + d 2 2 2 + d 1 2 1 + d 0 Question: What is the range of unsigned numbers you can represent with . .. ? 6 University of Florida, EEL 3701 – File 06 © Drs. Schwartz & Arroyo Low High How Many?
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This note was uploaded on 09/11/2010 for the course EEL 3701c taught by Professor Gugel during the Spring '05 term at University of Florida.

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06 - 31-Aug-102:23 PM Math EEL 3701 EEL 3701 Menu Review of...

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