Question #194396

Implement the following Boolean function only by using decoders and OR gate.

F(A,B,C,D) = ∑ (1,2,4,7,10,11,13,15)

Expert's answer

*Given Boolean function is:

F(A,B,C,D)= (1,2,4,7,10,11,13,15)

*Here function have 4input- A,B,C,D

SO we will use a 4:16 decoder to implement this function

*here, OR gate is also used,so its the case of Active HIGH output

*Its Implementation as follows

*Decoder is nothing but a logical circuit that takes n-input and decodes it and produce

output.

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How To implement it?

and-1)first count the number of inputs given in Function.

in above example F(A,B,C,D),there are 4 input

2)Select type of decoder to implement it, i.e.**,n: decoder**

**that's why here we used,4:16 decoder**

** **3)draw the respective decoder

4)Now, among the decoder outputs, select only the output number included in Function. Then through these, connect OR gate to produce final output as function.

here,output involves minterm of 1,2,4,7,10,11,13,15

so select them and connect with OR gate to implement the given function.

Thus, in this way, the given Boolean function is implemented with decoder and OR gate.

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