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Lecture 8: Binary Multiplication & Division - University of …

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!

Division 1001ten Quotient Divisor 1000ten | 1001010ten Dividend-1000 10 101 1010-1000 10ten Remainder At every step, • shift divisor right and compare it with current dividend • if divisor is larger, shift 0 as the next bit of the quotient • if divisor is smaller, subtract to get new dividend and shift 1 as the next bit of the quotient

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