Binary Values and Number Systems

2.4 Binary Values and Computers

Numbers within the computer are represented in binary form. In fact, all information is somehow represented using binary values. The reason is that each storage location within a computer contains either a low-voltage signal or a high-voltage signal. Because each location can have only one of two states, it is logical to equate those states to 0 and 1.

  • A low-voltage signal is equated with a 0.
  • A high-voltage signal is equated with a 1.

In fact, you can forget about voltages and think of each storage location as containing either a 0 or a 1. Note that a storage location cannot be empty: It must contain either a 0 or a 1.

Recall that each storage unit is called a binary digit, or bit for short. Bits are grouped together into bytes (8 bits), and bytes are grouped together into units called words.

The number of bits in a word is known as the word length of the computer. For example, IBM 370 architecture in the late 1970s had

  • half words (2 bytes or 16 bits),
  • full words (4 bytes),
  • double words (8 bytes).

Modern computers are often 32-bit machines (such as Intel's Pentium IV processor) or 64-bit machines (such as Hewlett-Packard's Alpha processors and Intel's Itanium 2 processor).

However, some microprocessors that are used in applications such as pagers are 8-bit machines. The computing machine you are using, whatever it is, is ultimately supported by the binary number system.