Chapter 6: Difference between revisions

Revision as of 19:28, 23 March 2010

Boolean Algebra
A	B	NAND ${\overline {AB}}$	NOR ${\overline {A+B}}$	XOR $A\oplus B$
0	0	1	1	0
0	1	1	0	1
1	0	1	0	1
1	1	0	0	0

"If the variables in a logic expression are replaced by their inverses, and if the AND operation is replaced by OR, the OR operation is replaced by AND, and the expression is inverted, the resulting logic expression yields the same values as before the changes."<ref>Electronics p.353</ref>
It is possible to create any combinatorial logic function with solely NAND (or NOR) gates

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-===Digital Logic===
+===Digital Logic Gates===
 {| class="wikitable" border="1" style="text-align:center"
 |+Boolean Algebra
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 |}
-*'''NAND Equivalent Gates'''
+===De Morgan Laws & NAND Equivalent Gates===
+*"If the variables in a logic expression are replaced by their inverses, and if the AND operation is replaced by OR, the OR operation is replaced by AND, and the expression is inverted, the resulting logic expression yields the same values as before the changes."<ref>Electronics p.353</ref>
-:*Inv: <math>\overline{AA}=\overline{A}</math>, Nand with the inputs tied together
+*It is possible to create any combinatorial logic function with solely NAND (or NOR) gates
-:*AND: <math>\overline{(\overline{AB})}</math>, NAND followed by and Inv
-:*OR: <math>\overline{(\overline{A} \, \overline{B})}=A+B</math>
+:*Inv: <math>\overline{A}=\overline{AA}</math>
+:*AND: <math>AB=\overline{(\overline{A}+\overline{B})}</math>
-*De Morgan Laws
+:*OR: <math>A+B=\overline{(\overline{A} \, \overline{B})}</math>
-:*
-:*
+===References===
+<references/>