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# 2011) - Mallard Intro to Computer Engineering I Written...

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Written Hwk #9 (due 3/30/2011) ECE 290 Problem Set #9 Due: March 30, 2011 Problem 9.1 Consider a 3-bit twisted ring counter consisting of 3 D flip-flops (labelled C, B, A from left-to-right) and an inverter, connected such that DB = QC, DA = QB, and DC = QA'. Starting with state QCQBQA = 111, give the counting sequence in binary. a. Which states are illegal? Verify that the circuit is not self-correcting by showing the count sequence(s) for these illegal states. b. Modify the DC input to be DC = QCQB' + QA'. Verify that this modified circuit is self-correcting. c. Problem 9.2 Implement a mod 6 counter which counts in the following CBA sequence and repeats: 111, 010, 100, 001, 101, 000. I.e., the counter proceeds through its 6 states in the (nonstandard) order 7, 2, 4, 1, 5, 0. Draw the state diagram for this counter. Note: There are no "input/output" labels on the edges, because there is no input (other than the clock) and the output is just the state. a. You will implement the counter using 3 T flip-flops. Draw the next state/excitation table, showing the current state CBA, the next state C + B + A + , and the flip-flop excitation inputs T C T B T A . b. Give the K-maps and provide minimal SOP expressions for T C , T B , T A . c. Draw the augmented state diagram; i.e., include the don't care states. Is this counter self-starting? Explain. d. Modify your circuit so that, from any don't care state, the next state will be 000. Show your work. Hint: Go back to part (c) to make the necessary changes. e. Problem 9.3 Design a 4-bit register, whose inputs and outputs are as shown in the diagram below. The mode operation table is also given under the diagram. M 0 M 1 M 2 Operation 0 0 0 No Change 0 0 1 Logical Shift Right 0 1 0 Logical Shift Left 0 1 1 Increment value by 1 1 0 0 Clear all bits 1 0 1 Complement all bits 1 1 0 Arithmetic Shift Right 1 1 1 Parallel Load Use D flip-flops to implement the PISO (Parallel-in Serial-Out) shift register. You can use this as a block N in your final design.

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