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Main points of this past exam are: Latch and Mux, Counting Your Blessings, Transparent Latches, DesignToggle, Clock Inputs, Toggle Enable, Clear Signal, LabelSignals, Enable Inputs, Assume Clock Inputs
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4 problems, 5 pages Exam Three 17 November 2099
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1 2 3 4 total
4 problems, 5 pages Exam Three 17 November 2099
Problem 1 (2 parts, 25 points) Counting Your Blessings
Part A (12 points) Design a toggle cell using only transparent latches, a 4-to-1 mux, and an inverter. Use icons for the latch and mux. Your toggle cell should have an active high toggle enable input TE , and an active low clear input -Clear , clock inputs Φ 1 and Φ 2 , and an output Out. Label all signals. The clear signal should take precedence over the toggle enable.
I (^0) I (^1) I (^2) I (^3) S 1 S 0
Out
En
In Out
En
In Out
Part B (13 points) Now combine three of these toggle cells to build a divide by five counter. Your counter should have active high external clear and external count enable inputs, a max count and three count outputs O 2 , O 1 , O 0. Be sure your design can be cascaded. Use any basic gates (AND, OR, NAND, NOR, & NOT) you require. Assume clock inputs to the toggle cells are already connected.
4 problems, 5 pages Exam Three 17 November 2099
Problem 3 (2 parts, 20 points) State Machine
Part A (15 points) Using the following state table, complete the state diagram below. Use correct state diagram notation. S variables are the current state. NS variables are the new state. X and Y are inputs while A is an output.
S 1 S 0 Y X NS 1 NS 0 A S 1 S 0 Y X NS 1 NS 0 A 0 0 X 0 0 0 0 1 0 X 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 X 0 0 1 0 1 1 X 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1
Part B (5 points) Suppose the primary output of this state machine is S 1 and S 0. Briefly describe what this state machine does.
4 problems, 5 pages Exam Three 17 November 2099
Problem 4 (2 parts, 25 points) A Logic Approach
Part A (10 points) Using only pass gates and inverters, design a four to one multiplexer. Label the inputs I 0 , I 1 , I 2 , I 3 , S 1 , and S 0. Label the output Out. For a clearer picture, only attach the control signal for the active high control input of the pass gates.
Part B (15 points) Assuming X controls S0 and Y controls S1, determine the multiplexer input values (LF 3 -LF 0 ) needed to produce the listed logical functions.
Y X out 0 0 LF 0 0 1 LF 1 1 0 LF 2 1 1 LF 3
logical function LF 3 LF 2 LF 1 LF 0