We examine the relationship between the abstract structure of a boolean algebra and the practical problem of creating logic networks for solving problems. There is a fundamental equivalence between Truth Functions, Boolean Expressions, and Logic Networks which allows us to pass from one to the other.
Two light switches, one light!
The problem is as follows: A light at the bottom of some stairs is controlled by two light switches, one at each end of the stairs. The two switches should be able to control the light independently. How do we wire the light?
Practice 11, p. 492/485
Exercise 10, p. 503/495
Exercise 1b, p. 501/493
Exercise 2, p. 502/493
We can use properties of Boolean algebra to simplify the canonical form, creating a much simpler logic network as a result.
Practice 11, p. 492/485
Half-Adders and Full-Adders
Half-Adder: Adds two binary digits.
Note, however, that the half-adder doesn't implement s in this way: instead,
Questions:
Full-Adder: Adds two digits plus the carry digit (made up of two half-adders, essentially!).
, 
, 
to the sum digit s
of a half-adder of , , to get 
.
, compare carry digits of both half-adders, to see
if either gives a 1 (in which case 
).
Practice 12, p. 496/490