Tutorial Slides for Week 8 ENEL 353: Digital Circuits — Fall 2015 Term Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary 27 October, 2015
slide 2/10 ENEL 353 F15 Tutorial Slides for Week 8 Topics for today 5-variable K-maps. Problems on multiplexers. Review: tristate buffers. Review: addition and overflow.
slide 3/10 ENEL 353 F15 Tutorial Slides for Week 8 Review: A 3-d map for a 5-variable problem We can visualize the 32-cell map this way: We look for vertical adjacencies as well as the horizontal adjacencies we’re used to finding in 4-variable maps. But marking and grouping 1-cells in a sketch like that is pretty much impossible . . .
slide 4/10 ENEL 353 F15 Tutorial Slides for Week 8 Review: 2-d representation of the 3-d map F ( A , B , C , D , E ) B C 00 01 11 10 D E 00 01 B C 00 01 11 10 D E 11 00 10 01 11 top layer: A = 0 10 bottom layer: A = 1 The five yellow cells are all adjacent to the blue cell.
slide 5/10 ENEL 353 F15 Tutorial Slides for Week 8 Exercise 1: 5-variable K-map problem Find a minimal SOP expression for the function represented by these K-maps: B B B C B C 00 01 11 10 00 01 11 10 D E D E 00 1 1 00 1 1 01 1 1 01 1 E E 11 1 11 1 D D 10 1 1 10 1 1 C C A = 0 A = 1
slide 6/10 ENEL 353 F15 Tutorial Slides for Week 8 Exercise 2: Multiplexer-based logic (2) Implement F with a 4:1 A B C Y mux, with A and C connected 0 0 0 0 as follows. You may add a NOT 0 0 1 1 gate if one is necessary. 0 1 0 0 S 1 = A S 0 = C 0 1 1 0 1 0 0 1 1 0 1 0 D 0 00 1 1 0 1 D 1 01 1 1 1 0 Y (1) Show how F can be D 2 10 implemented with an D 3 8:1 mux. 11
slide 7/10 ENEL 353 F15 Tutorial Slides for Week 8 Exercise 3: More multiplexer-based logic Find an SOP expression for Y , first using only algebra, then using a truth table. S 1 = A S 0 = B C 00 ¯ C 01 Y ¯ C 10 11
slide 8/10 ENEL 353 F15 Tutorial Slides for Week 8 Exercise 4: A 2013 midterm problem (i) (ii) A A B B C C Y Y D D Which of the following is true? Give clear reasons. (a) Contention is possible in circuit (i) but not in circuit (ii). (b) Contention is possible in circuit (ii) but not in circuit (i). (c) Contention is possible in both circuits. (d) Contention is not possible in either circuit.
slide 9/10 ENEL 353 F15 Tutorial Slides for Week 8 Exercise 5: Review of addition and overflow Suppose the two inputs to a 4-bit adder are 1011 and 1111. (a) To add the bit patterns, do you need to know whether they are being used as unsigned integers or as two’s-complement integers? (b) What are the outputs of the 4-bit adder? (c) Was there signed overflow? Unsigned overflow? Give reasons for your decisions. (d) Repeat (b) and (c) for inputs 0011 and 0110.
slide 10/10 ENEL 353 F15 Tutorial Slides for Week 8 Next week No quiz! Exercises related to ◮ timing of combinational logic ◮ basic sequential logic elements
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