Question: 4. A state machine has one input x(t) and two-bit state (Q 1 (t), Q 0 (t)). The machine is described by the following state
4. A state machine has one input x(t) and two-bit state (Q1(t), Q0(t)). The machine is described by the following state equations.
Q1(t + 1) = Q0(t) + x(t) Q1(t)
Q0(t + 1) = Q1 (t) + x(t)Q0(t)
y(t) = Q1(t)Q0(t)
Use two JK flip-flops and a minimal two-level NAND network to implement the machine.
(i). Write the state excitation table and draw the state diagram.
(ii). Show your derivation (K maps) and draw the logic diagram.
(i).
I started this table, I am not sure how to fill in the rest or if it is entirely correct so far.
| Id | Q1(t) | Q0(t) | x | J1(t) | J0(t) | K1(t) | K0(t) | Q1(t+1) | Q0(t+1) | y |
| 0 | 0 | 0 | 0 |
|
|
|
| 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
|
|
|
| 0 | 1 | 0 |
| 2 | 0 | 1 | 0 |
|
|
|
| 1 | 1 | 0 |
| 3 | 0 | 1 | 1 |
|
|
|
| 1 | 1 | 0 |
| 4 | 1 | 0 | 0 |
|
|
|
| 0 | 0 | 0 |
| 5 | 1 | 0 | 1 |
|
|
|
| 0 | 0 | 0 |
| 6 | 1 | 1 | 0 |
|
|
|
| 1 | 0 | 1 |
| 7 | 1 | 1 | 1 |
|
|
|
| 1 | 1 | 1 |
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