Let's take a quick review of all that we have learned about number systems.

  1. We began by introducing the binary number system and discussing the importance of binary numbers to computers. We learned that the binary number system is the language which the computer understands.

  2. We began learning how to speak the binary language by comparing it with a language we already understand: the decimal system. We learned how to convert between binary and decimal, how to perform binary arithmetic, and how to represent signed numbers. We discovered that we can perform all of our arithmetic operations using only addition and a special representation for signed numbers. This fact allows computer engineers to simplify the design of computer processors.

  3. We examined two other number systems: octal and hexadecimal. These number systems have a special relationship to the binary system because their bases are powers of 2. This relationship makes conversion from binary to octal or hexadecimal and vice versa quite simple. For this reason, octal and hexadecimal are often used as a shorthand for writing long binary numbers.