CODEWITHSUNDEEP
logiclogical-operators
angel_30
angel_30

Reputation: 1

Using AND or OR logic gates to construct a 4-variable function

I'm a software developer, and I'm trying to model a function using only AND or OR gates. I remember having similar subjects in my undergraduates, but I don't recall it. f(x,y,z,w) is a function of four variables, and gets True when AT LEAST two of the variables gets true. How can I visually construct it using only AND or OR gates?

UPDATE: I think f= xy+xz+xw+yz+yw+zw if I'm correct!

Upvotes: 1

Views: 249

Answers (1)

Tim Biegeleisen
Tim Biegeleisen

Reputation: 521289

The following expression is logically what you want: 

(xy) + (xz) + (xw) + (yz) + (yw) + (zw)
x (y + z + w) + y (z + w) + (zw)

Note that you don't need to check for cases of three or four TRUE values, because they are already included in the check for two TRUE values.

I represent AND gates with scalar multiplication, and OR gates using the addition operator (+). Note that when you wire up the actual circuit you might even be able to simplify even more than I have by reusing pieces (e.g. z + w).

Upvotes: 1

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