created: 07/04/96; 2^{nd} edition: 03/20/01;
corrected 09/19/01; audio: 12/12/03; revised 05/19/15

Base 16 is often
used to represent integers.
Integers represented in base 16 are said
to be represented with **hexadecimal** notation.
The hexadecimal representation of an integer is
equivalent to the pattern name of the bits in the
binary representation of the integer.

It is easy to convert the representation of an integer between binary and hexadecimal. Converting representations between decimal and an arbitrary base is somewhat more difficult. The chapter presents some algorithms for doing this.

**Chapter Topics:**

- Left and right shifts
- Unsigned binary representation
- Familiar binary integers
- Hexadecimal representation
- Equivalence of hexadecimal representation and bit pattern names
- Converting representations from hexadecimal to binary
- Converting representations from decimal to any base

A particular number is represented by 1010 (binary representation). What is the number represented in base ten?