How a memoryless counter can be used as a ROM? Design a 4-bit synchronous counter using J-K flip-flops. Implement the following Boolean function using 4:1 multiplexer using A and B variables to the selection lines. F(A, B, C) = √(2, 3, 7)

Q.) How a memoryless counter can be used as a ROM? Design a 4-bit synchronous counter using J-K flip-flops. Implement the following Boolean function using 4:1 multiplexer using A and B variables to the selection lines. F(A, B, C) = √(2, 3, 7)

 Subject: Digital Electronics

How a Memoryless Counter Can Be Used as a ROM

A memoryless counter can be used as a Read-Only Memory (ROM) by treating the counter's output as addresses for the ROM. Each count represents a unique address that can be used to access a specific data word stored in the ROM. Here's a step-by-step approach to using a counter as a ROM:

  1. Define the ROM Content: Determine the data that needs to be stored in the ROM. Each data word corresponds to a unique address.

  2. Design the Counter: Create a counter that can cycle through all the addresses needed to access the ROM content.

  3. Map Counter Outputs to ROM Addresses: Connect the counter outputs to the address inputs of the ROM. Each state of the counter will select a different address in the ROM.

  4. Read Data from ROM: As the counter increments, the ROM outputs the data word stored at the address specified by the counter.

Designing a 4-bit Synchronous Counter Using J-K Flip-Flops

A 4-bit synchronous counter can be designed using J-K flip-flops by connecting them in such a way that the output of one flip-flop triggers the next flip-flop in the sequence. Here's how to design it:

  1. Understand J-K Flip-Flop Operation: The J-K flip-flop has two inputs (J and K) and two outputs (Q and Q'). When the clock input (CLK) is triggered, the state of the Q output is determined by the J and K inputs according to the following table:

| J | K | Q(next state) | |---|---|---------------| | 0 | 0 | No change | | 0 | 1 | Reset (0) | | 1 | 0 | Set (1) | | 1 | 1 | Toggle |

  1. Connect J-K Flip-Flops: To create a counter, connect the Q' output of each flip-flop to the J and K inputs of the next flip-flop in the sequence. For a 4-bit counter, you will need four J-K flip-flops.

  2. Set Up the Clock: Connect the clock input of all J-K flip-flops together so that they are triggered simultaneously.

  3. Initialize the Counter: Set the counter to the initial state (usually 0000) by resetting all flip-flops.

  4. Implement the Counter Logic: To make the counter count up, connect the J and K inputs of each flip-flop to a logic high (1). This will cause each flip-flop to toggle its output on each clock pulse.

Here's a schematic representation of the 4-bit synchronous counter:

CLK ----+----+----+----+
        |    |    |    |
       JK   JK   JK   JK
       FF   FF   FF   FF
        |    |    |    |
        Q0   Q1   Q2   Q3

Implementing the Boolean Function Using a 4:1 Multiplexer

To implement the Boolean function F(A, B, C) = √(2, 3, 7) using a 4:1 multiplexer with A and B as the selection lines, follow these steps:

  1. Understand the Function: The given function specifies that F is true for the minterms 2, 3, and 7. In binary, these minterms correspond to (010), (011), and (111), respectively.

  2. Set Up the Multiplexer: A 4:1 multiplexer has four data inputs (D0, D1, D2, D3), two selection inputs (S1, S0), and one output (Y). Connect A to S1 and B to S0.

  3. Determine the Data Inputs: Since C is the only variable that changes for each input combination, use it to determine the values of the data inputs:

| S1 | S0 | Minterm | F(A, B, C) | Data Input | |----|----|---------|------------|------------| | 0 | 0 | 0 | 0 | D0 = 0 | | 0 | 1 | 1 | 0 | D1 = 0 | | 1 | 0 | 2 | 1 | D2 = C | | 1 | 1 | 3 | 1 | D3 = C |

  1. Connect the Data Inputs: Connect D0 and D1 to logic 0, and connect D2 and D3 to the C input.

  2. Read the Output: The output Y of the multiplexer will now represent the function F(A, B, C).

Here's a schematic representation of the multiplexer implementation:

        A (S1)
        | B (S0)
        | |
       4:1 MUX
    D0 | | | | Y = F(A, B, C)
    D1 | | | |
    D2 | | | |
    D3 | | | |
       | | | |
       0 0 C C

In summary, the counter serves as a ROM address generator, the 4-bit synchronous counter is designed using J-K flip-flops with a simple toggle configuration, and the Boolean function is implemented using a 4:1 multiplexer with A and B as selection lines and C connected to the relevant data inputs.