Algorithmic Problem Solving with Python

Аннотация

At their core, computers are remarkably simple devices. Nearly all computers today are built using electronic devices called transistors. These transistors serve as switches that behave much like simple light switches—they can be on or they can be off. In a digital computer each bit of information (whether input, memory, or output) can be in only one of two states: either off or on, or we might call these states low or high, or perhaps zero or one. When we say “bit,” we have in mind the technical definition. A bit is a binary digit that can be either 0 or 1 (zero or one). In a very real sense computers only “understand” these two numbers. However, by combining thousands or millions or even billions of these transistor switches we can achieve fantastically complicated behavior. Thus, rather than keeping track of a single binary digit, with computers we may be able to work with a stream of bits of arbitrary length. For each additional bit we use to represent a quantity, we double the number of possible unique values the quantity can have. One bit can represent only two “states” or values: 0 and 1. This may seem extremely limiting, but a single bit is enough to represent whether the answer to a question is yes or no or a single bit can be used to tell us whether a logical statement evaluates to either true or false. We merely have to agree to interpret values consistently, for example, 0 represents no or false while 1 represents yes or true. Two bits can represent four states which we can write as: 00, 01, 10, and 11 (read this as zero-zero, zero-one, one-zero, one-one). Three bits have eight unique combinations or values: 000, 001, 010, 011, 100, 101, 110, and 111. In general, for n bits the number of unique values is 2n.