2: Review of Binary Arithmetic

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One of the major goals of computer science is to use abstraction to insulate the users from how the computer works. For instance, computers can interpret speech and use natural language processing to allow novice users to perform some pretty amazing tasks. Even programming languages are written to enhance the ability of the person writing the code to create and support programs, and a goal of most modern languages and systems is to be hardware agnostic.

Abstraction is a very positive goal, but it hides the fact that some level all computers are just machines. While HLLs abstract and hide the underlying hardware, they must be translated into assembly language to use the hardware. Everything in a computer, even seemingly intelligent operations like understanding speech, is run as a set of mechanical steps on a very small machine called a CPU.

One of the goals of a computer science education is to allow a student to at least metaphorically understand the existence and purpose of these levels; to strip away all of the levels of abstraction and make the workings of the computing machine explicit. Without an understanding of a computer as a machine, even the best programmer, system administrator, support staff, etc., will have significant gaps in what they are able to accomplish. A basic understanding of hardware is important to any computer professional.

Learning assembly language is different than learning a HLL. Assembly language is intended to directly manipulate (or mechanically control) the hardware that a program is run on. It does not rely on the ability to abstract behavior, instead giving the ability to specify exactly how the hardware is to work to the programmer. Therefore, it uses a very different vocabulary than a HLL. That vocabulary is not composed of statements, variables and numbers but of operations, instructions, addresses, and bits.

In assembly it is important to remember that the actual hardware to be used only understands binary values 0 and 1. To begin studying assembly, the reader must understand the basics of binary and how it is used in assembly language programming. The chapter is written to help the reader with the concepts of binary numbers.