c ha COPY Number Systems and Codes igital systems are built from circuits that process binary digits- 0s very few real-life problems are based on binary numbers or any numbers at all.Therefore,a digital system designer must establish some correspondence between the bina- familiar numeric quantities can be represented and manipulated in a digital system,and how nonnumeric data,events,and conditions also can be epresented The first nine sections describe binary number systems and show how addition,subtraction,multiplication,and division are performed in these systems.Sections 2.10-2.13 show how other things,such as decimal num- bers,text characters,mechanical positions,and arbitrary conditions,can be encoded using strings of binary digits. Section 2.14 introduces"n-cubes,"which provide a way to visualize the relationship between different bit strings. The n-cubes are especially useful in the study oferror-detecting codes in Section 2.15.We conclude the chapter with an introduction to codes for transmitting and storing data one bit at a time : Copyright 1999 by John F.Wakerly Copying Prohibited 21DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Copyright © 1999 by John F. Wakerly Copying Prohibited 21 chapter 2 Number Systems and Codes igital systems are built from circuits that process binary digits— 0s and 1s—yet very few real-life problems are based on binary numbers or any numbers at all. Therefore, a digital system designer must establish some correspondence between the bina￾ry digits processed by digital circuits and real-life numbers, events, and conditions. The purpose of this chapter is to show you how familiar numeric quantities can be represented and manipulated in a digital system, and how nonnumeric data, events, and conditions also can be represented. The first nine sections describe binary number systems and show how addition, subtraction, multiplication, and division are performed in these systems. Sections 2.10–2.13 show how other things, such as decimal num￾bers, text characters, mechanical positions, and arbitrary conditions, can be encoded using strings of binary digits. Section 2.14 introduces “n-cubes,” which provide a way to visualize the relationship between different bit strings. The n-cubes are especially useful in the study of error-detecting codes in Section 2.15. We conclude the chapter with an introduction to codes for transmitting and storing data one bit at a time. D