Since childhood, we have learned to do our computations using the numbers 0 - 9, the digits of the decimal number system. In fact, we are so accustomed to working with decimal numbers that we hardly think about their use. We balance our checkbooks, pay monthly bills, and even solve algebra homework with the aid of the decimal number system. Considering the widespread use of this system, why should anyone bother to study the binary number system? The answer is found in something that is almost as widespread as decimal numbers: computers.

While it is fine for us to use ten digits for our computations, computers do not have this luxury. Every computer processor is made of millions of tiny switches that can be turned off or on. Since these switches only have two states, it makes sense for a computer to perform its computations with a number system that only has two digits: the binary number system. These digits (0 and 1) are called bits and correspond to the off/on positions of the switches in the computer processor. With only these two digits, a computer can perform all the arithmetic that we can with ten digits.

Our study of the binary system will help us gain a better understanding of how computers perform computations. In a way, we can think of this study as learning another language, the language of the computer. Every instruction that a computer executes is coded in this binary language. The goal of our study is to become fluent in the language of the computer by learning the following skills:

• Converting between binary and decimal,
• Performing binary arithmetic,
• Representing signed binary numbers, and
• Performing binary arithmetic with signed numbers.