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If we know the position x of t of an object as a function of time, we can use differentiation to calculate its velocity and its acceleration at later times. Essentially, by taking the derivatives of the position, we know everything there is to know about the motion. Sometimes, however, we'll want to go in the other direction. We'll have the acceleration as a function of time and we'll want to find the velocity as a function of time, or the position as a function of time. We'll use a technique called integration, and let's see how that works. To begin with, suppose we have a constant acceleration. So our acceleration a of t is some constant a 0. In that case, we know that this constant acceleration can be written as the change in velocity delta v over some time interval delta t, and therefore that the change in velocity delta v over some time interval delta t can just be written as a 0 acceleration, the constant acceleration, times the elapsed time delt...

We're now in a position to define our what it means to be a digital processing element. We say a device is a "combinational device" if it meets the following four criteria: First, it should have digital inputs, by which we mean the device uses our signaling convention, interpreting input voltages below V_L as the digital value 0, and voltages above V_H as the digital value 1. Second, the device's outputs should also be digital, producing outputs of 0 by generating voltages less than or equal to V_L and outputs of 1 by generating voltages greater than or equal to V_H. With these two criteria, we should be able to hook the output of one combinational device to the input of another and expect the signals passing between them to be interpreted correctly as 0's and 1's. Next, a combinational device is required to have a functional specification that details the value of each output for every possible combination of digital values on the inputs. In the...