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State Diagram, State table, State assignment, Excitation table and maps
written 4.9 years ago by gravatar for teamques10 teamques10 ★ 64k modified 2.2 years ago by gravatar for sagarkolekar sagarkolekar ★ 11k
digital logic design
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written 2.2 years ago by gravatar for sagarkolekar sagarkolekar ★ 11k

mod-6 synchronous counter using T f/f

mod - 6 counter has 6 states.

Hence, the number of f/f's is,

$2^n \gt N \gt 2^n-1$

$\therefore 2^3 \gt 6$

$\therefore$ Number of flip-flops required = 3

Step 1: State Diagram.

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Step 2: State table.

present state (Ps) Next state (Ns)
a b
b c
c d
d e
e f
f a

Step 3: State assignment.

a = 000, b = 001, c = 010, d = 011, e = 100, f = 101.

Step 4: Excitation table of Tf/f and truth table of T f/f

Truth table.

T $Q_n+1$
0 $Q_n$
1 $Q_n$

Excitation table.

$Q_n$ $Q_n+1$ T
0 0 0
0 1 1
1 0 1
1 1 0

Step 5: Excitation table and maps.

| Present state (Ps) | Next state (Ns) | Excitation inputs | |----|----|----|

q2 q1 q0 Q2 Q1 Q0 T2 T1 T0
0 0 0 0 0 1 0 0 1
0 0 1 0 1 0 0 1 1
0 1 0 0 1 1 0 0 1
0 1 1 1 0 0 1 1 1
1 0 0 1 0 1 0 0 1
1 0 1 0 0 0 1 0 1
1 1 0 x x x x x x
1 1 1 x x x x x x

Step 6: Simplifying logic expressions.

enter image description here

$T_2 = q_1 q_0 + q_2 q_0$

enter image description here

$T_1 = q_2 q_0$

enter image description here

$\therefore T_o = 1$

enter image description here
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