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A scale factor of 1 ⁄ 10 cannot be used here, because scaling 160 by 1 ⁄ 10 gives 16, which is greater than the greatest value that can be stored in this fixed-point format. However, 1 ⁄ 11 will work as a scale factor, because the maximum scaled value, 160 ⁄ 11 = 14. 54, fits within this range. Given this set:
Order of magnitude is a concept used to discuss the scale of numbers in relation to one another. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. [1] For example, 1 and 1.02 are within an order of magnitude.
Addition of a pair of two's-complement integers is the same as addition of a pair of unsigned numbers (except for detection of overflow, if that is done); the same is true for subtraction and even for N lowest significant bits of a product (value of multiplication). For instance, a two's-complement addition of 127 and −128 gives the same ...
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Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...
Subtraction also obeys predictable rules concerning related operations, such as addition and multiplication. All of these rules can be proven, starting with the subtraction of integers and generalizing up through the real numbers and beyond. General binary operations that follow these patterns are studied in abstract algebra.
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