10.A sequential circuit has two JK flip-flops A and B, two inputs x and y, and one output z. The flip-flop input equations and circuit output equation are J₁ = A' x + B' y K₁ = Bx' y' Js = A' xy K₁ = A' + B' x = = A' x' B' y' a. Fill in the next-state table given below. B X JA K₁ y J₁ Ks B (t + A A(t + 1)

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b. Derive the simplified state equations for A(t+1) and B
(t + 1).
Transcribed Image Text:b. Derive the simplified state equations for A(t+1) and B (t + 1).
10.A sequential circuit has two JK flip-flops A and B, two inputs
x and y, and one output z. The flip-flop input equations and
circuit output equation are
J₁ = A' x + B' y
K₁ = Bx' y'
+ B' x
Js = A' xy
Ks = A'
z = A' x'
+ B'y'
a. Fill in the next-state table given below.
B
X
y
JA
КА
JB
K₁
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
(1)
1
1
1
0
1
0
1
(2)
1
1
0
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
(5)
0
0
0
0
0
0
1
(3)
1
0
0
1
1
0
0
0
(9)
A(t +
1)
0
1
1
1
0
0
1
1
1
1
1
1
(7)
1
1
1
B (t +
0
0
0
1
0
0
0
0
0
1
1
(8)
1
Transcribed Image Text:10.A sequential circuit has two JK flip-flops A and B, two inputs x and y, and one output z. The flip-flop input equations and circuit output equation are J₁ = A' x + B' y K₁ = Bx' y' + B' x Js = A' xy Ks = A' z = A' x' + B'y' a. Fill in the next-state table given below. B X y JA КА JB K₁ 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 (1) 1 1 1 0 1 0 1 (2) 1 1 0 A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 (5) 0 0 0 0 0 0 1 (3) 1 0 0 1 1 0 0 0 (9) A(t + 1) 0 1 1 1 0 0 1 1 1 1 1 1 (7) 1 1 1 B (t + 0 0 0 1 0 0 0 0 0 1 1 (8) 1
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