definitions

literal: a variable or its complement
minterm ("of n variables"): a product of n literals in which each variable appears exactly once in either true or complemented form, but not both
(in a truth table, a minterm has a value of one for exactly one combination of values of the variables A,B,C)
maxterm: a maxterm of n variables is a sum of n literals in which each variable appears exactly once in either true or complemented form
maxterm expansion == standard product of sums: a function f written as a product of maxterms
minterm expansion = standard sum of products: writing a function f as a sum of minterms
functionally complete: any boolean function can be expressed in terms of this set of operations
e.g. and, or, not
e.g. NAND
e.g. NOR
in order to determine if is functionally complete, msop; if no complement ==> NOT cannot be realized and it is NOT functionally complete
minimum sum of products: a sum of product terms which has (a) a minimum number
of terms, (b) of all those expressions which have the same miniumum number of
terms, has a minimum number of literals
minimum product of sums: a product of sum terms which (a) has a minimum number
of factors, (b)of all those expressions which have the same number of factors,
has a minimum number of literals.
implicant: any single 1 or group of 1's which can be combined together on a
map of the function F represents a product term which is called an implicant
of F
prime implicant: a product term which cannot be combined with another term to
eliminate a variable.

nand and nor

the output of a NAND gate is 1 iff one or more of its inputs are zero
F = (abc)' = a' + b' + c'
F = (a + b + c)' = a'b'c' ==> NOR --> all inputs are 0, is true
sop ==> and-or => NAND => or-nand -> or-nor
pos ==> or-and => nor-nor => and-nor => nand-and
to draw NAND from AND-OR circuit, replace all gates with NAND gates (invert single inputs to level 1,3,...)
the alternative NAND gate formulation is an or gate with inverted inputs (bubbled inputs)
to convert to nand or nor
1. convert all AND gates to NAND gates by adding an inversion buble at the output, and all OR gates to NAND by adding inversion bubbles at the inputs
2. do the opposites for conversion to NOR gates (invert AND inputs and OR outputs)
3. if the bubbles, don't cancel, place an inverter between the gates or if it's the input of a single literal, simply complement it.