1. (A). Trace the counting sequence for the circuit below. Draw the state diagram. 111 100 101 110 0 00 0

2. (B). Design a counter with sequence of 0, 1, 2, 3, 4 using T, D, and J-K, respectively. Complete the state diagram by verifying the behaviors of illegal states. Are your designs self-starting? CBAC + B + A + T C T B T A D C D B D A j C k C j B k B j A k A 000 001 010 011 100 101 110 111 001 010 011 100 000 XXX 001 011 001 111 100 XXX 001 010 011 100 000 XXX 0X0X1X 0X1XX1 0XX01X 1XX1X1 X10X0X XXXXXX Truth table:

3. 11

4. (T) 100 000 010 001 011 111 110 101 (D) 100 000 010 001 011 111 110 101

5. (JK) 100 000 010 001 011 111 110 101

6. (C). Repeat the design by directing the illegal states to 011. 100 000 010 001 011 110 101 111

7. CBAC + B + A + T C T B T A D C D B D A j C k C j B k B j A k A 000 001 010 011 100 101 110 111 001 010 011 100 000 011 001 011 001 111 100 110 101 100 001 010 011 100 000 011 0X0X1X 0X1XX1 0XX01X 1XX1X1 X10X0X X11XX0 X1X01X X1X0X0 Truth table: T C =BA+C T B =C’A+B’A T A =BA’+C’

8. 0010 0000 CB A C B 0 1 1101 0110 A C B 0 1100 0111 A C B 0 1 1 D C =C’BA+C’A D B =AC+BA’+B’A D A =AC+BA’+A’C’ XX10 XX00 CB A C B 0 1 1XX1 0XX0 A C B 0 XXXX 0111 A C B 0 1 1 j C =BA j B =A j A =B+C’ 11XX 11XX CB A C B 0 1 X01X X00X A C B 0 0011 XXXX A C B 0 1 1 k C =1 k B =C’A k A =C’