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Arithmetic Intro Computer Organization 1 Computer Science Dept Va Tech February 2008 © McQuain Algorithm for Integer Division The natural (by-hand) algorithm for integer division is essentially an iterated subtract-and-shift. Recall that mathematics says: or: where:
Arithmetic Intro Computer Organization 2 Computer Science Dept Va Tech February 2008 © McQuain Division Illustrated 15 divided by 6: | ^^^^ 0000 < 0110 no go ^^^ ^ 0001 < 0110 no go ^^ ^^ 0011 < 0110 no go ^ ^^^ 0111 >= 0110 OK, set quotient bit and subtract ^^^^ 0011 < 0110 no go, and done divisor remainder quotient * # negative, retract, shift # negative, retract, shift # negative, retract, shift # OK, keep remainder, shift # negative, retract, shift
Arithmetic Intro Computer Organization 3 Computer Science Dept Va Tech February 2008 © McQuain Division Design 1.0 Divisor Shift right 64-bit ALU 64 bits Remainder Write 64 bits Quotient Shift left Control test 32 bits Look familiar??
Arithmetic Intro Computer Organization 4 Computer Science Dept Va Tech February 2008 © McQuain Division Design 2.0 Just as with multiplication, we can optimize the hardware to eliminate most of the 64-bit components used in the first design. Divisor 32-bit ALU Remainder Write Shift right Control test 32 bits 64 bits Shift left
Division & Divisibility. a divides b if a is not zero there is a m such that a.m = b a is a factor of b b is a multiple of a a|b Division.
Mod arithmetic. a mod m is the remainder of a divided by m a mod m is the integer r such that a = qm + r and 0 <= r < m again, r is positive Examples.
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This has been made by Frederick M. Groth What is Partial Quotients? It is a method to solve division problems. This is how to do it. 4/381=? First choose.
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Dividing by Whole Numbers Lesson 3-8. In long division, we use both multiplication and division.
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Dividing Decimals by Whole Numbers. In long division, we use both multiplication and division.
Factoring Polynomials of Higher Degree. To review: What is the remainder when you divide x 3 – 4x 2 – 7x + 10 by x – 2? Divisor Quotient Dividend Remainder.
Weve looked at linear and quadratic functions, polynomial functions and rational functions. We are now going to study a new function called exponential.
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