Question

In: Computer Science

5. a) Draw a state diagram for a sequential circuit that outputs a 1 if and...

5. a) Draw a state diagram for a sequential circuit that outputs a 1 if and only if its single

input has completed the sequence 1111.

b) Then build the circuit using D flip-flops and any necessary gates. NO Overlap is

Allowed.

6. Repeat question 5 but this time OVERLAP IS ALLOWED:

Expert Solution

5 (a) State Diagram:

state table:

Present State	Next state (X = 0)	Next State (x = 1)
a	a/0	b/0
b	a/0	c/0
c	a/0	d/0
d	a/0	a/1

Let

a : y₀= 0 y₁= 0
b : y₀= 0 y₁= 1
c : y₀= 1 y₁= 0
d : y₀= 1 y₁= 1

Truth Table:

	y₀	y₁	X	Y₀	Y₁	Z
a	0	0	0	0	0	0
a	0	0	1	0	1	0
b	0	1	0	0	0	0
b	0	1	1	1	0	0
c	1	0	0	0	0	0
c	1	0	1	1	1	0
d	1	1	0	0	0	0
d	1	1	1	0	0	1

K-MAP:

Layout:

	^X'	X
y^'₀y₁	0	1
y^'₀y₁	2	3
y₀y₁	6	7
y₀y^'₁	4	5

K-map Groups:

For Y₀

(3)	y^'₀y₁X
(5)	y₀y^'₁X

Boolean expression: Y₀ = y^'₀y₁X + y₀y^'₁X = X(y^'₀y₁ + y₀y^'₁) = X (y₀ XOR y₁)

Groups For Y₁:

(1,5)

y'₁X

Boolean expression: Y₁ = y'₁X

Groups for Z:

(7)

y₀y₁X

Boolean expression: Y₁ = y₀y₁X

(b) Circuit using D Flip flop:

(6)

(a) State Diagram:

State Table:

Present State	Next state (X = 0)	Next State (x = 1)
a	a/0	b/0
b	a/0	c/0
c	a/0	d/0
d	a/0	d/1

Truth Table:

	y₀	y₁	X	Y₀	Y₁	Z
a	0	0	0	0	0	0
a	0	0	1	0	1	0
b	0	1	0	0	0	0
b	0	1	1	1	0	0
c	1	0	0	0	0	0
c	1	0	1	1	1	0
d	1	1	0	0	0	0
d	1	1	1	1	1	1

K-MAP:

K-map Groups:

For Y₀

(3,7)	y₁X
(5,7)	y₀X

Boolean expression: Y₀ = y₁X + y₀X = X(y₀ + y₁)

Kmap groups for Y₁:

(1,5)	y^'₁X
(5,7)	y₀X

Boolean expression: Y₁ = y₁X + y₀X = X(y₀ + y^'₁)

Kmap groups for Z:

(7)

y₀ y₁X

Boolean expression: Z = y₀ y₁X

(b) Circuit Diagram:

venereology answered 3 years ago

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