Perhaps the most natural use of computers is to perform arithmetic operations. Even a simple calculator can add, subtract, multiply, and divide numbers. This leads to the following question: how are numbers stored in a calculator?
You have probably heard the claim that “computers only manipulate zeros and ones.” In particular, this claim implies that computers use only zeros and ones to represent numbers. In other words, numbers (as well as everything else) are represented by sequences of zeros and ones.
In this chapter we show how natural numbers (i.e., nonnegative integers) can be represented by sequences of zeros and ones. The representation we use is called binary representation. Our main goal in this ...