HW6_solution

# HW6_solution - SOLUTION 1 ECE 2504 Introduction to Computer...

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Unformatted text preview: SOLUTION 1 ECE 2504 Introduction to Computer Engineering, Fall 2009 Homework 6 Due date: 11 Oct 09, 11:55pm Show all work. Use LogicWorks to draw circuit diagrams. 1. (6 pts) A sequential circuit has one JK flip flop, two inputs x and y, and one output S. The circuit consists of a full adder connected to the flip flop in the following way. J > K Q Q FA Y X Z S C Y X S Write the flip flop input equations Complete the state table. Hint: A full adder truth table is shown in section 1-5 in Mano. J=K=(xy + (x ⊕ y)z) ′ Note: This is equivalent to the following (xy)’((x ⊕ y)z)’ (x’+y’)( (x ⊕ y)’+z’) x’(x ⊕ y)’ + x’z’ + y’(x ⊕ y)’ + y’z’ x’(xy+x’y’) + x’z’+ y’(xy+x’y’) + y’z’ x’xy + x’x’y’ + x’z’ + xyy’ + x’y’y’ + y’z’ J=K = x’y’ + x’z’ + y’z’ Present State Inputs Intermediate Signals** FF Inputs Next State Output Q X Y Z C C’=J=K Q(t+1) S 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 **Not truly part of the state table, but included here for clarity. SOLUTION 2 2. (5 pts) Draw the state diagram for a 3-bit counter that counts down using the following sequence (seven, six, five, four, three, two, one, zero, seven, …) when the input x=1 and holds...
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HW6_solution - SOLUTION 1 ECE 2504 Introduction to Computer...

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