To design a two-bit counter circuit that counts from 00 to 10 and ignores the state 11 using J-K flip-flops, you can follow these steps:
State Transition Diagram:
```
+-------+ J0 +-------+
| |-------->| |
| 00 | K0 | 01 |
| |<--------| |
+-------+ +-------+
^ | J1 +-------+
| +---------| |
+-----------| 10 |
| K1 | |
+-----------+-------+
```
Karnaugh Maps for J and K Inputs:
For J0 and K0:
```
K0J0
----
00 | 0 0
01 | 1 0
10 | 0 1
11 | - -
```
For J1 and K1:
```
K1J1
----
00 | 1 0
01 | 0 0
10 | 0 1
11 | - -
```
Boolean Expressions:
```
J0 = Q0'
K0 = Q0
J1 = Q0Q1'
K1 = Q0'Q1
```
Circuit Implementation:
You can implement this circuit using J-K flip-flops. Let's denote the flip-flop outputs as Q0 and Q1.
```plaintext
+---+ +---+
--|J0K0|----|J1K1|---
+---+ +---+
| |
| +-----|-----+
| | |
| | +--|-----+ +-----+
| | | | |---| |
| | +--|-----+ | 10 |
| | | | |
| +-----|---------| |
| | +-----+
+--------|-----------+
|
Q0Q1
```
This circuit uses two J-K flip-flops (J0K0 and J1K1) to implement the state transition diagram. The clock input is assumed to be a common clock signal shared by both flip-flops. The state changes according to the defined J and K inputs based on the current state.
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