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Here's a final logic implementation strategy using read-only memories. This strategy is useful when you need to generate many different outputs from the same set of inputs, a situation we'll see a lot when we get to finite state machines later on in the course. Where MUXes are good for implementing truth tables with one output column, read-only memories are good for implementing truth tables with many output columns. One of the key components in a read-only memory is the decoder which has K select inputs and 2^K data outputs. Only one of the data outputs will be 1 (or HIGH) at any given time, which one is determined by the value on the select inputs. The Jth output will be 1 when the select lines are set to the binary representation of J. Here's a read-only memory implementation for the 2-output truth table shown on the left. This particular 2-output device is a full adder, which is used as a building block in addition circuits. The three inputs to the functio...

PROFESSOR: The logic of predicates is a basic concept in mathematical language as well as being a topic on its own. In particular, I'm going to talk now about the idea of the two so-called quantifiers. For all-- that's the upside-down A. And exists-- that's the backward E. So what's a predicate? Basically, a predicate is a proposition, except it's got variables in it. Here's an example. P of x, y is the predicate that depends on x and y. And let's say it's defined to be x plus 2 equals y. Now, in order to figure out whether or not a predicate is true, I need to know the values of the variables-- in this case, x and y. So if I tell you that x is 1 and that y is 3, guess what? P of 1 and 3-- P of x and y when x is 1 and y is 3-- is true, because in fact, 1 plus 2 is equal to 3. If I tell you that x is 1 and y is 4, then since 1 plus 2 is not equal to 4, P of 1 and 4 is false. On the other hand, since P of 1 and 4 is false, that makes not P of...