2.1 Positional Number Systems Why do we discuss the number systems?> Digital systems only have two states. Sodigital circuits process binary digits. Butvery few real-life problems are based onbinary numbers.> A digital system designer must know howfamiliar numeric quantities can berepresented and manipulated in a digitalsystem, and how nonnumeric data, eventsand conditions are also can be representedReturnNext
2.1 Positional Number Systems Return Next n Why do we discuss the number systems? Ø Digital systems only have two states. So digital circuits process binary digits. But very few real-life problems are based on binary numbers. Ø 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
2.1 Positional Number SystemsExample for a decimal542.673=5.102+4:101+ 2:100 + 6.10-1 +7.10-2 + 3.10Where there arep digits, to left of thepoint and n digits tothe right of the point.dp-1 is the leftmost nonzero digit, calledhigh-order digit or most significant.d., is the rightmost nonzero digit, calledlow-order digit or least significant.ReturnBackNext
d-n is the rightmost nonzero digit, called low-order digit or least significant. Ø Example for a decimal 542.673=5·102+4·101+ 2·100 + 6·10-1 +7·10-2 + 3·10- 3 Where there are p digits, to left of the point and n digits to the right of the point. dp-1 is the leftmost nonzero digit, called high-order digit or most significant. Return Back Next 2.1 Positional Number Systems
2.1 Positional Number SystemsFor arbitrary number systemsSWeighted Sum3Weightr>2RadixCoefficient of Position i CiWhy is it called position number systemReturnBackNext
Ø For arbitrary number systems Weighted Sum S Radix r2 Coefficient of Position i ci Why is it called position number system? Weight r i Return Back Next 2.1 Positional Number Systems
2.1 Positional Number SystemsGeneral number systemsBinary number systemb, is the ith digitof a binary numbercalled bit. Binarynumber systemonly has two didits- 0 and 1.bp-1 is the leftmost nonzero digit, calledhigh-order digit or most significant bit(MSB)b-n is the rightmost nonzero digit, calledlow-order digit or least significant bit(LSB)BackNextReturn
Return Back Next Ø Binary number system n General number systems bp-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). bi is the ith digit of a binary number, called bit. Binary number system only has two didits –– 0 and 1. 2.1 Positional Number Systems
2.1 Positional Number SystemsOctal number systemOctal numbersystem has eightdigits 0 ~ 7.Hexadecimal number systemHexadecimal numbersystem has sixteendigits decimaldigits 0 ~ 9 andletters A~F.NextReturnBack
Return Back Next Ø Octal number system Octal number system has eight digits –– 0 ~ 7. Ø Hexadecimal number system Hexadecimal number system has sixteen digits –– decimal digits 0 ~ 9 and letters A~F. 2.1 Positional Number Systems