EDIT: I think I'm probably more confused than I realise. My question could also be phrased as "how was the given diagram constructed from the expression, particularly with reference to the OR gates?"

Say I have the logic expression X = A AND ((B AND C) OR (B AND D) OR (C AND D))

It looks like I need 3 OR gates to handle the possible conditions for the second input to the AND gate.

However, if I add brackets to the expression, like so:

X = A AND (((B AND C) OR (B AND D)) OR (C AND D))

it looks like I can reduce the number of OR gates to just 2.

Is this correct? Is this a standard method of simplifying expressions using the associative property of Boolean algebra?

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  • 2
    \$\begingroup\$ I see in both expressions only 2 OR gates \$\endgroup\$ Jan 6, 2020 at 16:43
  • \$\begingroup\$ yeah, it's unclear how you came to three OR gates. Care to elaborate? \$\endgroup\$ Jan 6, 2020 at 17:15

1 Answer 1


The first expression has one, 3-input OR gate. The second has two, 2-input OR gates. These two expressions are logically equivalent.

Whether either one is simpler than the other depends on your definition of simple. Does simple mean fewer gates or does simple mean that you only use 2-input gates? In the real world, optimization is usually done to minimize silicon area and propagation delays.


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