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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, simply add the negative number hence,sub

Lecture 8: Binary Multiplication & Division • Today’s topics: Addition/Subtraction Multiplication Division • Reminder: get started early on assignment 3. 2 2’s Complement – Signed Numbers 0000 0000 0000 0000 0000 0000 0000 0000two = 0ten

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