Transcription of Lecture 8: Binary Multiplication & Division
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Lecture 8: Binary Multiplication & Division
1 Lecture 8: Binary Multiplication & Division Today s topics: Addition/Subtraction Multiplication Division Reminder: get started early on assignment 322 s Complement Signed Numbers0000 0000 0000 0000 0000 0000 0000 0000two= 0ten0000 0000 0000 0000 0000 0000 0000 0001two= 1111 1111 1111 1111 1111 1111 1111two= 231-11000 0000 0000 0000 0000 0000 0000 0000two= -2311000 0000 0000 0000 0000 0000 0000 0001two= -(231 1) 1000 0000 0000 0000 0000 0000 0000 0010two= -(231 2)..1111 1111 1111 1111 1111 1111 1111 1110two= -21111 1111 1111 1111 1111 1111 1111 1111two= -1 Why is this representation favorable?Consider the sum of 1 and -2 .. we get -1 Consider the sum of 2 and -1 .. we get +1 This format can directly undergo addition without any conversions!Each number represents the quantityx31-231+ x30230+ x29229+ .. + x121+ x0203 Alternative Representations The following two (intuitive) representations were discardedbecause they required additional conversion steps beforearithmetic could be performed on the numbers sign-and-magnitude: the most significant bit represents+/- and the remaining bits express the magnitude one s complement: -x is represented by inverting allthe bits of xBoth representations above suffer from two zeroes4 Addition and Subtraction Addition is similar to decimal arithmetic For subtraction.
Multiplication Example Multiplicand 1000ten Multiplier x 1001ten-----1000 0000 0000 1000-----Product 1001000ten In every step • multiplicand is shifted • next bit of multiplier is examined (also a shifting step) • if this bit is 1, shifted multiplicand is added to the product. 7 HW Algorithm 1 ...
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