Question

Design 2 bits counter that count down by using T flip flop when input x =1 and counts up
when x=0. Find the following
1. Derive the state table
2. Derive the K‐map simplifications.
3. Draw the logic diagram

Answer 1

1. T flip flop excitation table:

State table:

INPUT	PRESENT STATE	NEXT STATE	FLIP FLOP T1	FLIP FLOP T0
X	Q1	Q0	Q1'	Q0'	T1	T0
0	0	0	0	1	0	1
0	0	1	1	0	1	1
0	1	0	1	1	0	1
0	1	1	0	0	1	1
1	0	0	1	1	1	1
1	0	1	0	0	0	1
1	1	0	0	1	1	1
1	1	1	1	0	0	1

The state diagram:

K-map simplifications:

T1= Q0' X + Q0 X'

T0 = 1

3. logic diagram: