Computer Science circuit question, help please? A circuit has the following equa

Question

Computer Science circuit question, help please?

A circuit has the following equation: G = abc + abc’ + cab. If you implemented the circuit as is, you would need three 3-input AND gates, one Inverter, and one 3-input OR gate. If you reduce the circuit to the minimal possible number of terms, what combination of logic gates would you need?

two 2-input AND gates and one 2-input OR gate

just one inverter

just one 3-input OR gate

just one 2-input AND gate

three 3-input AND gates, one Inverter, and one 3-input OR gate

none of the above

***DISREGARD this big box, I'm not sure why it appeared but I don't know how to delete it!***

two 2-input AND gates and one 2-input OR gate

just one inverter

just one 3-input OR gate

just one 2-input AND gate

three 3-input AND gates, one Inverter, and one 3-input OR gate

none of the above

***DISREGARD this big box, I'm not sure why it appeared but I don't know how to delete it!***

Explanation / Answer

4th option : just one 2-input AND gate

G = abc + abc’ + cab
G = a.b.c + a.b.c’ + c.a.b

a.b is common in all three terms. lets take them out common

G = a.b.(c+c'+c)

Now c+c' is always 1 (using the identity A + A' = 1)

G = a.b.(1+c)

Now 1+c is always 1 (using the identity 1 + A = 1)

G = a.b.(1) = a.b.1

Now use th eidentity A.1 = A

G = a.b

We have two inputs with AND relation

So, we need only one 2-input AND gate to implement the circuit

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