软硬件系统编程PPT (11).pdf

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1、二进制数的算术运算二进制数的算术运算Arithmetic Operations of Binary NumbersArithmetic Operations of Binary Numbers2DivisionAdditionSubtractionMultiplication31.Addition and subtraction of binary numbersAddition:Addition uses a form of carrying.Adding two 1 digits produces a digit 0,while 1 will have to be added to the

2、 next column0+0=0 0+1=1 1+0=1 1+1=0（carry 1）Subtraction:Subtraction uses a form of borrowing.Subtracting a 1 digit from a 0 digit produces the digit 1,while 1 will have to be subtracted from the next column.0-0=0 1-0=1 1-1=0 0-1=1（borrow 1）1 0 1 0 1 1 0 11 0 1 0 1 1 0 10 1 0 1 1 0 1 00 1 0 1 1 0 1 0

3、+)+)11 11 1 0 01 1 0 00 1 0 10 1 0 1-)1.011.1100000Multiplication00=0 01=0 10=0 11=1E.G.11001001=110110042.Multiplication of binary numbers1 1 0 01 1 0 01 0 0 11 0 0 1 )01010000000011001101100Partial ProductsMultiplication of binary numbersRule 1Multiplication can be converted into Addition and Shif

4、t5E.g.000010110100Rule 2 Every time the multiplier multiplied by 2,the multiplicand will shift one digit to the left in the product(Here 2 is the 10 in binary).=00101100BDivision00=0 01=0 11=1E.g.10011111063.Division of binary numbers110100111110110.10111110001101100=110.17DivisionRule 1Division can

5、 be converted into subtraction and shift operationsIn the computer,the subtraction operation can be converted into an addition operationE.g.000010110100=00000010BQuotient Reminder=11 BRule 2:Every time the dividend is divided by 2,the dividend will shift one digit to the right in the final result.(Here 2 is the 10 in binary)Summary1 1 1 1 1 1 1 11 1 1 1 1 1 1 10000000100000001+)+)1 100000000Computers use the binary number system for arithmetic operationsThe range of numbers that computers can represent is limitedOverflow