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ee101_hw7_sol

ee101_hw7_sol - EE 101 Homework 7 Redekopp Name_Solutions...

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1 EE 101 Homework 7 Redekopp Name: __Solutions______________________________ Due: Score: ________ 1. The goal is to find the state diagram following the steps in the class notes. (1) Find the excitation equations for S 0 , S 1 , R 0 and R 1 . S 0 = X R 0 = X’· Q 1 S 1 = X’· Q 0 R 1 = Q 0 ’ + X (2) Find the transition equations using SR Flip-flops. According to the characteristic equation of the SR Flip-flop, we get the transition equations below: Q 0 * = S 0 + R 0 ’·Q 0 = X + (X + Q 1 ’) · Q 0 = X + Q 1 ’·Q 0 Q 1 * = S 1 + R 1 ’·Q 1 = X’·Q 0 + Q 0 ·X’· Q 1 = X’·Q 0 (3) The equation for output of the state machine is: F = X · Q 1 · Q 0 (4) Construct transition/output table Current State Next State Output X = 0 X = 1 X = 0 X = 1 Q 1 Q 0 Q 1 * Q 0 * Q 1 * Q 0 * F 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0

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2 (5) Substitute symbolic state names for the codes Current State Next State Output X = 0 X = 1 X = 0 X = 1 State Next State Next State F SInit SInit SA 0 0 SA SB SA 0 0 SC SInit SA 0 1 SB SC SA 0 0 (6) Draw the state diagram SInit SA X = 0 SC SB X = 1 X = 1 X = 0 X = 1 X = 0 X = 0 X = 1 / F = 1 Following the state diagram, we find that this circuit is checking for the sequence: 1001. The waveform is below: CLK /RESET STATE F SInit X SA SB SC SA
3 2. (1) Find the excitation equations for J 0 , J 1 , K 0 and K 1 . J 0 = A XOR B K 0 = 0 J 1 = Q 0 ’· B K 1 = 0 (2) Find the transition equations using JK Flip-flops. According to the characteristic equation of the JK Flip-flop, we get the transition equations below: Q 0 * = J 0 · Q 0 + K 0 ’·Q 0 = (A XOR B ) · Q 0 + Q 0 Q 1 * = J 1 · Q 1 + K 1 ’·Q 1 = A·Q 1 ’·B’·Q 0 + Q 1 (3) The equations for outputs of the state machine are: EQ = Q

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ee101_hw7_sol - EE 101 Homework 7 Redekopp Name_Solutions...

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