Computer Science: Algorithms, Theory, and Machines

In 1936, Alan Turing published a paper that is widely hailed as one of the most important scientific papers of the 20th century. This lecture is devoted to the two far-reaching central ideas of the paper: All computational devices have equivalent computational power, and there are limitations to that power.

As computer applications expanded, computer scientists and mathematicians realized that a refinement of Turing's ideas is needed. Which computational problems can we solve with the resource limitations that are inescapable in the real world? As described in this lecture, this question, fundamentally, remains unanswered.

Every programmer needs understand the basic characteristics of the underlying computer processor being used. Fortunately, the fundamental design of computer processors has changed little since the 1960s. In this lecture, we provide insights into how your Java code actually gets its job done by introducing an imaginary computer that is similar to both the minicomputers of the 1960s and the microprocessor chips found in today's laptops and mobile devices.

Continuing our description of processor design and low-level programming, we provide context stretching back to the 1950s and discuss future implications of the von Neumann machine, where programs and data are kept in the same memory. We examine in detail the idea that we design new computers by simulating them on old ones, something that Turing's theory guarantees will always be effective.

Starting with a few simple abstractions (wires that can carry on/off values and switches that can control the values carried by wires), we address in this lecture the design of the circuits that implement computer processors. We consider gates that implement simple logical functions and components for higher-level functions, such as addition. The lecture culminates with a full circuit for an arithmetic/logic unit.

In this lecture, we provide the last part of our answer to the question "How does a computer work?" by developing a complete circuit for a computer processor, where every switch and wire is visible. While vastly different in scale, this circuit, from a design point of view, has many of the same characteristics as the circuits found in your computer and your phone.