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Understanding Floating Point Numbers and Binary Representation in Numerical Methods

Learn the fundamentals of floating point numbers and binary representation in numerical methods. Explore how to code floating point numbers using equations, understand binary representation, and work with recurrence functions.

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Understanding Floating Point Numbers and Binary Representation in Numerical Methods

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  1. NUMERICAL METHODS M. Antczak, S. Wąsik

  2. Floating point numbers are coded with using equation • x = s * 2c * m, • where • s – sign (+1,-1) • c – attribute (integer value) • m – floating point <1/2; 1) Example: / 2 -2 = -1 * 20 * 2 -1 * 21 * 1 / 2 -1 * 22 * 1/2 s = -1 c = 2 m=1/2

  3. Binaryrepresentation of floating point b1b2b3b4… • m = b1/2 + b2/4 + b3/8 + .. + bt/2t • where • t – number of bits Example (t = 5 bits): ≥ Yes 1 0 ≥ No ≥ Yes 1 0 0 ≥ No Finally: 10100 0 0 ≥ No

  4. Recurrence function example: recurrencestoppingcondition recurrencerule Example: n = 5 => silnia(5)  5 * silnia(4)  120  24  4 * silnia(3)  6  3 * silnia(2)  2 * silnia(1)  2  1

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