# Binary Values and Number Systems

## Binary Values and Number Systems

This section describes binary values, the way in which computer hardware represents and manages information.
By making sure we have an understanding of binary values, we pave the way to understanding how computing systems use the binary number system to accomplish their tasks.

After stydying this section, you should be able to:

• distinguish among categories of numbers.
• describe positional notation.
• convert numbers in other bases to base 10.
• convert base-10 numbers to numbers in other bases.
• describe the relationship between bases 2, 8, and 16.
• explain the importance to computing of bases that are powers of 2.

## 1 Numbers and Computing

Numbers are crucial to computing. In addition to using a computer to execute numeric computations, all types of information that we store and manage using a computer are ultimately stored as numbers.

At the lowest level, computers store all information using just the digits 0 and 1.

These digits are called bits (short for binary digits). Although you may be inclined to associate bits with numeric values, they are really only symbols whose meaning depends on the application at hand.

• Sometimes patterns of bits are used to represent numeric values;
• Sometimes they represent characters in an alphabet and punctuation marks;
• Sometimes they represent images;
• Sometimes they represent sounds.