Question

1. Design a 3 bit sequential circuit using T flip flops and one input X. When X = 0 the state of the circuit remains the same. When X = 1 the circuit goes through state transition from 0 -> 6 -> 2 -> 3 -> 5 -> 0. Make the state table, state equation and state diagram.

Need help trying to understand how to set up the truth table, should I use a JK truth table and go on or start from a T truth table, I'm confused, you don't have to answer the question entirely but help starting the question.

Answer 1

Designing a 3 bit sequential circuit using 3 D flip flops and one input X :

given that input x = 0 circuit remains same. and

when x = 1 next state transition from 0 -> 6 -> 2 -> 3 -> 5 -> 0 .

for given conditions the state table is odbtained shown below .

C001-01110-10001 B010-11-100 00111 A010 000-11-10-01 p x 011 | 0 1 0 1 0 1 0 1 010101 C001-1001-100110011 nt B000011110000111|

from above table state equations for all states are given below.

ABCx 00 01 1110 Οι 10 1x

state equation for next state A is D_A obtained from above table.

D_A = AX' + A'B'X + A'CX

ABC 00 01 11 10 01 1 11 11x1 10

state equation for next state A is D_B obtained from above table.

D_B = BX' + C'X

ABCx 00 01 1110 01 10

D_C = CX' + A'C + BC + A'BX.

The required design can be drawn using above table and the equations with AND , OR gates.

-> STATE DIAGRAM of this design :

when x = 0 each state transition to their own state and 001 , 100 and 111 states are don't care conditions for given input.

Here considering state diagram for X =1 without 001 , 100 and 111 states. which is given below.

010 x-1 浏 x=1 110 x=1 011 101