Question

Ex. 1] Design a counter that goes through the sequence 143 6 2 5 (and repeats) using 2 D flip-flops and 1 T flip-flop and gates needed (Note: account for any missing states).

the first picture is the question and the second picture is the solution. however i cannot understand the steps in the solution and dont know how the circuit was constructed. can you please explain the solution?

Answer 1

This is the random sequence counter. Here the given sequence is 1 4 3 6 2 5

We first draw the state diagram and then state table where we estimate next state based on present state.

And then we assign flipflops. Then we solve for flipflop inputs.

Here the given is 14 3625 sequence This is a random counter In the requence maximum carat i 6. so we need 3 bits to represent 6. So, the total no. of states are 8. tooes Starte o is the rest state. whenever the counter is in state In the next count should be '4' according to the given aequence. So, the next sterte would be 6! In the same way next states are anighed according the present steates for each count. prevent state Next state 001 000 001 101 010 tro 01 100 011 101 001 110 010 ool

use 2D flie y in the moblem they've asked to and sa T-flintlop. 4 Next state bits are of Q2 Q₃ .. Here they've wad 2D-ffs too for d, and for Q3 they've used Toff. Qz. and Qz values to T-f. " We case enign di values to Di and DQ w But for T we assign according to the truth table excitatim table. present state Next state T T will be 4 When zero, present state when they're and next state are some different T will belli 4 After that and then equations they've taken the min terms of Di, Ą PT. they've solved K-maps and got the for Di , D2 and T.

for Di Eml 1,2,3) Di= Q2 + Qi Q3 for Da Em (3, 4,6). a JO Da = or as to Qz az Dz = 0,03 + QT Qq Q3 for T mco, 1, 2, 3, 4) T= a zastą and gates are in 4 Aftur solving the K-maps they've used and Or' gatu for Di, Dz & T which sop form. Then they've given them to flip flops.

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