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I am self-studying the Nand2Tetris course. I am trying to simplify the Or logic gate as much as possible to simplify my HDL-specified circuit.

Using the Sum of Products, I write the following for the Or truth table:

(~A.B) + (A.~B) + (A.B)

= (~A.B) + (A).(B + ~B)

= (~A.B) + (A).(0)

= (~A.B) + 0

= ~A.B

However, the truth table of ~A.B isn't the same as the Or truth table, so I'm doing something wrong. I'm just not sure what it is. Please help : )

intelli78
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  • Write down the truth table for each row in the derivation, then you will see where exactly you made the mistake. – 5xum Sep 03 '14 at 08:07
  • you must not write down the whole truth table but only one of the rows of the truth table where they differ. for which A, B does the truth table differ? – miracle173 Sep 03 '14 at 08:09
  • @5xum Powerful technique, not sure why I didn't think to do that. Thanks. – intelli78 Sep 03 '14 at 08:16

1 Answers1

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Recall that the statement "$B$ is true or $B$ is false" is a tautology, so you should have gotten: \begin{align*} \overline AB + A\overline B + AB &= \overline AB + A(\overline B + B) \\ &= \overline AB + A(1) \\ &= \overline AB + A \\ \end{align*}

Adriano
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