l11_ece15a_6

l11_ece15a_6 - Combinational Logic Word Problems 1....

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1 ECE 15A Fundamentals of Logic Design Lecture 11 Malgorzata Marek-Sadowska Electrical and Computer Engineering Department UCSB 2 Combinational Logic Word Problems 1. Understand the problem what is the circuit supposed to do? write down inputs (data, control) and outputs draw block diagram or other picture 2. Formulate the problem in terms of a truth table or other suitable design representation 3. Follow implementation procedure K-maps, CAD tools (espresso, sis) 3 Process Line Control Problem ± Statement of the Problem: Rods of varying length (+/-10%) travel on conveyor belt, mechanical arm pushes rods within spec (+/-5%) to one side Second arm pushes rods too long to other side Rods too short stay on belt 3 light barriers (light source + photocell) as sensors ± Design combinational logic to activate the arms 4 Process Line Control Problem Where to place the light sensors A, B, and C to distinguish among the three cases? Understanding the Problem Inputs are three sensors, outputs are two arm control signals Assume sensor reads "1" when tripped, "0" otherwise Call sensors A, B, C Spec + 5% +10% Too Long ROD Spec + 5% -5% Within Spec ROD Spec - 10% Too Short ROD 5 Process Line Control Problem Assume that A detects the leading edge of the rod on the conveyor Assumptions •Rods are placed perpendicularly to the direction of belt’s motion. •Rods are pushed to one side of the belt. 6 Process Control Problem A to B distance place apart at specification - 5% A to C distance placed apart at specification +5% A B C Spectification -5% Specification + 5% Too Long Too Short Within Spec
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2 7 Process Control Problem Truth table and logic implementation "too long" = A B C (all three sensors tripped) "in spec" = A B C' (first two sensors tripped) A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Function X X X X too short X in spec too long 8 Binary coded decimal (BCD) Decimal symbol BCD symbol 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 Example: (526) = (0101 0010 0110) = (1000001110) 10 BCD 2 9 BCD to 7 Segment Display Controller Input : a 4 bit bcd digit Output : the control signals for the display 4 inputs A, B, C, D 7 outputs C0 — C6 Block Diagram BCD-to-7-segment control signal decoder 7-Segment display C 0 C 1 C 2 C 3 C 4 C 5 C 6 A B C D C 5 C 0 C 6 C 3 C 4 C 1 C 2 C 0 C 1 C 2 C 3 C 4 C 5 C 6 10 BCD to 7 Segment Display Controller Analysis for C0: BCD input: A B C D C 5 C 0 C 6 C 3 C 4 C 1 C 2 C 0 C 1 C 2 C 3 C 4 C 5 C 6 C0 = 1 for decimal inputs (0,2,3,5,6,7,8,9) A B C D 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 C0 = 0 for decimal inputs = (1,4) A B C D 0 0 0 1 0 1 0 0 11 BCD to 7 Segment Display Controller
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This note was uploaded on 01/20/2011 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.

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l11_ece15a_6 - Combinational Logic Word Problems 1....

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