Chapter 6

Digital Logic Gates

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

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>
• It is possible to create any combinatorial logic function with solely NAND (or NOR) gates

Gate	Symbol	NAND equivalent
Inverter	${\overline {A}}$	${\overline {AA}}$
AND	$AB$	${\overline {({\overline {A}}+{\overline {B}})}}$
OR	$A+B$	${\overline {({\overline {A}}\,{\overline {B}})}}$

References

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