The 3-to-8 binary decoder and OR gate are used to create a logic circuit that can convert three input signals (w1, w2, w3) into a single output signal. This is useful for implementing complex Boolean functions, such as f(w1,w2,w3), which can be broken down into simpler logic gates using the decoder and OR gate.
The 3-to-8 binary decoder takes three input signals and uses them to select one out of eight output lines. Each input signal represents a binary number with a possible value of 0 or 1. By using different combinations of these three input signals, the decoder can select any of the eight output lines, allowing for a wide range of possible outputs.
The OR gate is used to combine the outputs of the 3-to-8 binary decoder into a single output signal. This gate performs a logical operation where the output is true (1) if any of the inputs are true (1). This is essential for creating the desired output for f(w1,w2,w3) as it allows for the combination of multiple outputs from the decoder.
Using a 3-to-8 binary decoder and OR gate allows for a more efficient and compact implementation of f(w1,w2,w3) compared to using individual logic gates. It also simplifies the design process and reduces the number of components needed, making it a cost-effective solution.
One limitation is that the number of inputs and outputs is fixed at three and eight, respectively. This means that it may not be suitable for more complex functions with a larger number of inputs. Additionally, the decoder and OR gate can only perform specific logic operations, so it may not be suitable for all types of Boolean functions.