Question

Design a two bit down counter circuit that counts from 3 to 0. It should have states 11, 10, 01, and 00. The initial state of the counter may be assumed to be 11. The counter will be in following successive states: 11, 10, 01, 00, 11, 10, 01, 00, 11,... Use J-K flip flop to design the circuit. You must design the circuit using state transition diagram and Karnaugh's maps.

Answer 1

this cover by a mathematics textbook it is the circle by hundred degree

Answer 2

Steps to design synchronous 2-bit down counter

Step 1 : Identify number of bits and flip flop

Step 2 : Write excitation table of flip flop

Step 3 : Make state diagram and state table

Step 4 : Solve Boolean expression

Step 5 : Make circuit

2-bit synchronous down counter by JK flip flop

Step 1 : n = 2 bits , Flip Flop = JK flip flop

Step 2 : Excitation table of JK flip flop

Qₙ Qₙ₊₁ J K

0     0   0 x  

0     1    1  x

1      0   x  1

1      1    x  0

Step 3 : State diagram and state table

Present State   Next State   Required Excitations

     Q₁   Q₀            Q₁⁺   Q₀⁺         J₁   K₁      J₀   K₀      

      1      1               1       0           x     0       x     1

      1      0              0      1            x      1       1      x

      0     1               0     0            0     x       x     1

      0    0               1       1            1      x       1      x

Step 4 : Solve Boolean expression

Step 5 : Make circuit