writing an expression for a circuit in terms of a result of either 1's or 0s

we used to make a truth table for a circuit, right? Well, this chapter starts out with an example where we make the circuit first than half-fill in the truth table. This gives us 'f' column where there was just an a,b,c values before.

we then write out the algebraic expression which gives us the result we want,
so specifiyng '1' as the result in those columns will lead to an equation.

minterm and maxterm expansions

literal: a variable or its complement

minterm: is the rows for which the SOP is 1 (any single element has a value
of 1)
The rows of a truth are the minterms of the equation
i.e. the minterm is simply all rows for which the truth table yields a true value

maxterm:is the rows where the POS is 0

the rows start counting from zero

minterm and maxterm are complementing each other

find the maxterm expansion of f(a,b,c,d) = a'(b' + d) + acd'
1) add all terms to each of the POS so that all literals are in each POS
2) multiply out
3) change to 0 and 1 notation
4) minterm are the rows which match that way of thinking about the POS terms

design of binary adders and subtractors

thinking about binary adders and subtractors helps us understand what a truth
table can do for us. For example, it can give us the minterms. Now, if we
have multiple outputs (not just one value on the right of the truth table) we
can have multiple functions as output. (This knowledge is necessary to
understand PLAs and ROMs as well as simple multiple-output functions into one
circuit).

for example, re: binary adders/subtractors, one result is the sum column the
other is the carry column.