- #1
conorordan
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Homework Statement
[itex]R=(A \cdot \overline{B})+(\overline{A} \cdot B)[/itex]
Using Boolean algebra, including the complement relation [itex]D\cdot \overline{D}=0[/itex], convert R to a form that uses one NAND, one AND and one OR gate (a total of three gates).
Homework Equations
de Morgan's theorem...
[itex]\overline{A+B}=\overline{A}\cdot\overline{B}[/itex]
[itex]\overline{A \cdot B}=\overline{A} + \overline{B}[/itex]
The Attempt at a Solution
By some trial and error I arrived at this;
[itex](\overline{A}+\overline{B})\cdot(A+B)[/itex]
And then using the second of de Morgan's equations on the first OR I got to this;
[itex]\overline{A\cdot B}\cdot(A+B)[/itex]
Which works as a solution, it has one NAND, one AND and one OR, however, I can't just skip to that bit, it's the working out in between that I'm missing, I'm not sure how to fill in the gaps.
Thanks for any help you can offer!