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# Class Note for ENGIN 112 at UMass(29)

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COURSE
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TYPE
Class Notes
PAGES
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KARMA
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This 18 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 11 views.

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Date Created: 02/06/15
ENGIN 112 Intro to Electrical and Computer Engineering Lectu re 1 3 Combinational Design Procedure quot ELECTRICAL 9 quot COMPUTER ENGINEERING umvsnswv or MASSACHUSETTS AMHERST ENGN11Z L13 Cnmhinminnzl Dvsign Prncedure 0dnher12 3 Overview Design digital circuit from specification Digital inputs and outputs known Need to determine logic that can transform data Start in truth table form Create Kmap for each output based on function of inputs Determine minimized sumofproduct representation Draw circuit diagram ENGN112 L13 Combinational Design Procedure October 1 2003 Design Procedure Mano Design a circuit from a specification 1 Determine number of required inputs and outputs 2 Derive truth table 3 Obtain simplified Boolean functions 4 Draw logic diagram and verify correctness A B C LS 0 0 0 0 0 0 0 1 01 sABC 0 1 0 01 RABC 0 1 1 01 1 0 0 01 1 0 1 01 1 1 0 01 ENGN112 L13 C b39 1139 ID 39 P dure 1 1 1 1 1 October1 2003 Previously we have learned 0 Boolean algebra can be used to simplify expressmns but not obVIous how to proceed at each step or if solution reached is minimal 0 Have seen five ways to represent a function Boolean expression truth table logic circuit mintermsmaxterms Karnaugh map ENGN112 L13 Combinational Design Procedure October 1 2003 Combinational logic design Use multiple representations of logic functions Use graphical representation to assist in simplification of function Use concept of don t care conditions Example encoding BCD to seven segment display Similar to approach used by designers in the field ENGN112 L13 Combinational Design Procedure October 1 2003 BCD to Seven Segment Display Used to display binary coded decimal BCD numbers using seven illuminated segments BCD uses 0 s and 1 s to represent decimal digits 0 9 Need four bits to represent required 10 digits Binary coded decimal BCD represents each decimal digit with four bits 0 0000 7 0 1 1 1 8 1 0 0 0 9 1 0 0 1 ENGN112 L13 Combinational Design Procedure October 1 2003 BCD to seven se ment displa List the segments that should be illuminated for each digit O abcdef 1 bc 2 abdeg 3 abcdg b 4 bcfg 5 acdfg quot 6 acdefg C 7 abc 8 abcdefg 9 abcdfg ENGN112 L13 Combinational Design Procedure October 1 2003 BCD to seven segment display Derive the truth table for the circuit Each output column in one circuit Inputs Outputs Dec w X y z a b c d e 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 2 0 0 1 0 1 1 0 1 1 7 0 1 1 1 0 0 ENGN112 L13 Combinational Design Procedure October 1 2003 BCD to seven segment display Find minimal sumofproducts representation for each output For segment a yz WX 00 01 11 10 Note Have only 00 1 0 1 1 lled in ten 01 0 1 1 1 squares corresponding to 11 the ten numerical 10 1 1 digits we Wish to represent ENGN112 L13 Combinational Design Procedure October 1 2003 Don t care conditions BCD display Fill in don t cares for undefined outputs Note that these combinations of inputs should never happen Leads to a reduced implementation For segment a yz WX 00 01 11 10 00 1 O 1 1 Put in don t care and interpret as 01 0 1 1 1 either 1 or O as 11 X X X X desired 10 1 1 X X ENGN112 L13 Combinational Design Procedure October 1 2003 Don t care conditions BCD display Circle biggest group of 1 s and Don t Cares Leads to a reduced implementation CC 939 For segment a yZ WX 00011110 00 1 01 0 Falzy 11 X 10 1 ENGN112 L13 Combinational Design Procedure October 1 2003 Don t care conditions BCD display Circle biggest group of 1 s and Don t Cares Leads to a reduced implementation CC 939 For segment a yz WX 00 01 11 10 00 1 O 1 1 010 1 1 1 11 X X 1011 gtltgtlt ENGN112 L13 Combinational Design Procedure October 1 2003 Don t care conditions BCD display Circle biggest group of 1 s and Don t Cares All 1 s should be covered by at least one implicant CC 939 For segment a YZ yz wx 00 01 11 10 W 00 01 11 10 001 O 1 1 001 0 1 1 01 0 1 1 1 01 0 1 1 1 11 X X X X 11 X X X X 101 X X 10 1 1 X X F882 Fa4XZ ENGN112 L13 Combinational Design Procedure October 1 2003 Don t care conditions BCD display Put all the terms together Generate the circuit C 939 For segment a yz WX 00 011110 F yw 2xz 00 1 0 1 1 01 O 1 1 1 11 X X X X 10 1 1 X ENGN112 L13 Combinational Design Procedure October 1 2003 Example of seven segment display decoding Cot to reset eounter to Decoded Seven zero after 9 3 segment dtsptay Segment 5 of 2 undecoded seven m segment dtsptay 4 OsctHator to Hz5U generate dock stgna 1 HZ Logo oot to decode segment a as per notes Hmt Seteot a component and tnen ousn 7 from mam menu bar to get We on wnat tnat component does and now t Works ENGN11Z L13 Cnmhinminnzl Dvsign Prncedure 0dnher12 3 BCD to seven segment display Derive the truth table for the circuit Each output column in one circuit Inputs Outputs Dec w X y z a b c d e 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 2 0 0 1 0 1 1 0 1 1 7 0 1 1 1 0 0 ENGN112 L13 Combinational Design Procedure October 1 2003 BCD to seven segment display Find minimal sumofproducts representation for each output For segment b yz W 00 01 11 10 See if you 00 1 1 1 1 complete this 01 1 0 1 0 example 11 10 1 1 ENGN112 L13 Combinational Design Procedure October 1 2003 Summary Need to formulate circuits from problem descriptions 1 Determine number of inputs and outputs 2 Determine truth table format 3 Determine Kmap 4 Determine minimal SOP 0 There may be multiple outputs per design 0 Solve each output separately 0 Current approach doesn t have memory 0 This will be covered next week ENGN112 L13 Combinational Design Procedure October 1 2003

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