Implement the Exclusive-OR function using PROM.

I. Introduction

The Exclusive-OR (XOR) function is a fundamental operation in digital logic. It is a binary operation that takes two binary inputs and returns a binary output. The output is true (or '1') if and only if the number of true inputs is odd. In other words, the XOR function returns true if the inputs are different, and false if they are the same.

Programmable Read-Only Memory (PROM) is a type of digital memory that is used to store binary information. The information stored in PROM can be programmed using a special device. Once programmed, the information can be read any number of times, but it cannot be changed. This makes PROM useful for storing permanent data, such as the firmware of a device.

II. Detailed Explanation of XOR function

The XOR function, also known as the 'exclusive or' function, is defined as follows:

XOR(A, B) = (A AND (NOT B)) OR ((NOT A) AND B)

This means that the XOR function returns true if A is true and B is false, or if A is false and B is true. In other words, the XOR function returns true if A and B are different.

The truth table of the XOR function is as follows:

III. Detailed Explanation of PROM

PROM is a type of digital memory that can be programmed to store specific binary information. Each cell in a PROM chip can store one bit of information. The information is programmed into the PROM by burning fuses in the chip. Once a fuse is burned, it cannot be unburned, which means that the information stored in the PROM is permanent.

The inputs to the PROM are used to select a specific cell in the chip. The output of the PROM is the binary value stored in the selected cell.

IV. Implementation of XOR function using PROM

To implement the XOR function using PROM, we need to program the PROM so that it stores the truth table of the XOR function. The inputs to the PROM will be the inputs to the XOR function, and the output of the PROM will be the output of the XOR function.

Here is how we can program the PROM:

1. For the input combination (0, 0), we program the PROM to store the value 0.
2. For the input combination (0, 1), we program the PROM to store the value 1.
3. For the input combination (1, 0), we program the PROM to store the value 1.
4. For the input combination (1, 1), we program the PROM to store the value 0.

V. Diagram of XOR function using PROM

A diagram is necessary to illustrate the implementation of the XOR function using PROM. The diagram should show the PROM chip with its inputs and output. The inputs should be labeled A and B, and the output should be labeled XOR(A, B). The diagram should also show how the fuses in the PROM are burned to store the truth table of the XOR function.

VI. Example

Let's consider an example where the inputs to the XOR function are A = 1 and B = 0. According to the truth table of the XOR function, the output should be 1.

When we apply these inputs to the PROM, it selects the cell that was programmed for the input combination (1, 0). This cell was programmed to store the value 1, so the output of the PROM is 1. This shows that the PROM correctly implements the XOR function.

VII. Conclusion

The XOR function can be implemented using PROM by programming the PROM to store the truth table of the XOR function. This method is simple and reliable, but it has some limitations. The main limitation is that the information stored in the PROM is permanent and cannot be changed. This means that if we want to implement a different function, we need to use a different PROM chip. Despite this limitation, the use of PROM is a common and effective method for implementing digital logic functions.

Summary

The Exclusive-OR (XOR) function is a fundamental operation in digital logic. It takes two binary inputs and returns a binary output. PROM (Programmable Read-Only Memory) is a type of digital memory that can be programmed to store binary information. The XOR function can be implemented using PROM by programming the PROM to store the truth table of the XOR function.

Analogy

Implementing the XOR function using PROM is like using a permanent storage device to store the results of a comparison between two inputs. It is similar to using a locked box to store a key that can only be accessed if the inputs are different.