老師導論課課件lecture

1、Number systems, operations, and codesA Symbolic ImageBoethius(波愛修斯) and Pythagoras(畢達哥拉斯 ) in a mathematical competition. Pythagoras uses an abacus, while Boethius uses numerials from India. Boethius looks very proud, he is ready while the poor Pythagoras still tries to find the solution.“It seems t

2、o us that after the invention of writing, the largest discovery was the use by humanity of the so-called decimal notation.” -M. V. Ostrogradsky3What does 5132.13 really mean?Depends on the number base!Assuming base 10:(5132.13)10 = 5x103 + 1x102 + 3x101 + 2x100 + 1x10-1 + 3x10-2 Assuming base 6:(513

3、2.13)6 = 5x63 + 1x62 + 3x61 + 2x60 + 1x6-1 + 3x6-2=(1136.25)10We often use a subscript to indicate the base.Number SystemsDecimal numbersThe position of each digit in a decimal number indicates the magnitude of the quantity represented and can be assigned a weight.Example5236.71 = 51000 + 2100 + 310

4、 + 61 + 70.1 + 10.01= 5103 + 2102 + 3101 + 6100 + 710-1 + 110-2The binary system with its two digits is a base-two system.5Binary numbersFigure 21 Illustration of a simple binary counting application. 6A simple binary counting applicationMost digital systems process binary data in groups that are mu

5、ltiples of four bits. Each hexadecimal digit represents a 4-bit binary number.Widely uses in computer and microprocessor applicationsDigits：09，A(10)，B(11)，C(12)，D(13)，E(14)，F(xiàn)(15).7Hexadecimal NumbersBinary-to-decimal conversionsAdding the weights of all 1s in a binary number to get the decimal valueDecimal-to-binary conversions8Conversions9Conversion from decimal to binary10Binary-to-hexadecimal conversionHexadecimal-to-binary conversionConversion between hexadecimal and binaryQuestions（101011.011）B（ ）D（65.4）D（ ）B（ ）H（8F.FF）H（ ）B Ques