Tutorial Slides for Week 8 ENEL 353: Digital Circuits Fall 2015 - - PowerPoint PPT Presentation

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

ENEL 353 F15 Tutorial Slides for Week 8

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Topics for today

5-variable K-maps. Problems on multiplexers. Review: tristate buffers. Review: addition and overflow.

ENEL 353 F15 Tutorial Slides for Week 8

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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 . . .

ENEL 353 F15 Tutorial Slides for Week 8

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Review: 2-d representation of the 3-d map

00 01 11 10 00 01 11 10 00 01 11 10 B C 00 01 11 10 D E bottom layer: A = 1 top layer: A = 0 F(A,B,C,D,E) B C D E

The five yellow cells are all adjacent to the blue cell.

ENEL 353 F15 Tutorial Slides for Week 8

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Exercise 1: 5-variable K-map problem

Find a minimal SOP expression for the function represented by these K-maps:

A = 0 A = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 00 01 11 10 B C D E B C 00 01 11 10 E D 00 01 11 10 B C D E B C 00 01 11 10 E D

ENEL 353 F15 Tutorial Slides for Week 8

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Exercise 2: Multiplexer-based logic

A B C Y 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1) Show how F can be implemented with an 8:1 mux. (2) Implement F with a 4:1 mux, with A and C connected as follows. You may add a NOT gate if one is necessary.

00

D0 D1

01 10

D2 D3

11

Y S0 =C S1 =A

ENEL 353 F15 Tutorial Slides for Week 8

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Exercise 3: More multiplexer-based logic

Find an SOP expression for Y , first using only algebra, then using a truth table.

00

C ¯ C

01 10

¯ C

11

Y S0 =B S1 =A

ENEL 353 F15 Tutorial Slides for Week 8

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Exercise 4: A 2013 midterm problem

A B C D Y

(ii)

A B C D Y

(i) 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.

ENEL 353 F15 Tutorial Slides for Week 8

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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.

ENEL 353 F15 Tutorial Slides for Week 8

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Next week No quiz!

Exercises related to

◮ timing of combinational logic ◮ basic sequential logic elements