2.1 Positional Number Systems ReturnNext Why do we discuss the number systems?  Digital systems only have two states. So digital circuits process binary digits. But very few real-life problems are based on binary numbers.  A digital system designer must know how familiar numeric quantities can be represented and manipulated in a digital system, and how nonnumeric data, events, and conditions are also can be represented.

d -n is the rightmost nonzero digit, called low-order digit or least significant.  Example for a decimal =5 · · · · · · Where there are p digits, to left of the point and n digits to the right of the point. d p-1 is the leftmost nonzero digit, called high-order digit or most significant. NextBackReturn 2.1 Positional Number Systems

 For arbitrary number systems Weighted Sum S Radix r  2 Coefficient of Position i c i Why is it called position number system? Weight r i NextBackReturn 2.1 Positional Number Systems

NextBackReturn  Binary number system General number systems b p-1 is the leftmost nonzero digit, called high-order digit or most significant bit(MSB). b -n is the rightmost nonzero digit, called low-order digit or least significant bit(LSB). b i is the i th digit of a binary number, called bit. Binary number system only has two didits –– 0 and Positional Number Systems

NextBackReturn  Octal number system Octal number system has eight digits –– 0 ~ 7.  Hexadecimal number system Hexadecimal number system has sixteen digits –– decimal digits 0 ~ 9 and letters A~F. 2.1 Positional Number Systems

 Example What are the octal values of the four 8-bit bytes in the 32-bit number ?  bit, byte, word, and nibble bit –– one binary digit is called bit. byte –– 8 binary digits is called byte. word –– n-bit word means one word has n binary digits. nibble –– 4- bit or half - byte is called nibble. BackReturn 2.1 Positional Number Systems Answer