ece15_11_2012_6

ece15_11_2012_6 - Combinational Logic Word Problems General...

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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 General Design Procedure 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, Q-M, a CAD tool 3 Example: 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 Example (cont.) Where to place the light sensors A, B, and C to distinguish among the three cases? Assume that A detects the leading edge of the rod on the conveyor 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 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 6 Truth table and logic implementation "too long" = A B C (all three sensors tripped) "in spec" = A B C' (first two sensors tripped) 0 0 0 1 X 0 0 A BC 0 1 00 01 11 10 0 0 0 0 X 1 0 0 A BC 0 1 00 01 11 10 Arm 1 (in spec) Arm 2 (too long) 0 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 - - - - too short - in spec too long
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2 7 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 (16) 10 = (0001 0110) BCD = (10000) 2 8 Example: BCD to 7 Segment Display Controller Understanding the problem: 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
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ece15_11_2012_6 - Combinational Logic Word Problems General...

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