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13 Computational Cost of Arithmetic

# 13 Computational Cost of Arithmetic - 13 The Computational...

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Cost of Arithmetic - 1 13 - The Computational Cost of Basic Arithmetic Operations All computers are designed to efficiently perform the four basic arithmetic operations: add, subtract, multiply and divide. Addition is easy because there are only two binary digits, 0 and 1. These are the rules: 0+0=0 0+1=1 1+0=1 1+1=0 Real numbers are added by first "aligning" the fractional parts (i.e., by equating the exponents), and then adding the fractions together and, when necessary, updating the exponent. Using the rules established above, it can be easily verified that 1 0 0 0 1 0 1 0 1 + 1 1 1 1 1 1 _________________ 1 0 1 0 1 0 1 0 0 Subtraction, in most computers is the same as addition. In other words, x-y=x+(-y). The basic multiplication rules for binary integers are: 0*0=0 0*1=0 1*0=0 1*1=1 You can multiply long binary numbers together the same way you multiply numbers in base 10 using a pen and paper. (However, there exist faster multiplication algorithms which will not be discussed here.) To multiply floating point numbers, you multiply the mantissas and add the exponents.

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13 Computational Cost of Arithmetic - 13 The Computational...

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