Explain each of the following concepts, along with at least one suitable example for each: (i) Fixed-point number representation (ii) round-off error (iii) representation of zero as floating point number (iv) significant digits in a decimal number representation (v) normalized representation of a floating point number (vi) overflow
(i) Fixed-point number representation: Fixed-point representation is a method of storing real numbers by fixing the number of digits after (and sometimes before) the decimal point. It is useful for applications requiring fast computation and limited precision. For example, in 8-bit fixed-point format with 4 bits for the integer part and 4 bits for the fractional part, the number 5.25 would be represented as 0101.0100. This method is ___ _________ ____ _______ _______ ________ _________ _____ ________ _______ _______.
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For the following data develop difference table and find forward differences and backward differences
| I | xi | yi |
| 0 | -1 | 16.8575 |
| 1 | 0 | 24.0625 |
| 2 | 1 | 16.5650 |
| 3 | 2 | -13.9375 |
| 4 | 3 | 28.5625 |
| 5 | 4 | 144.0625 |
Express A³fi as a central difference.
Explain each of the following concepts, along with at least one suitable example for each: (i) Fixed-point number representation (ii) round-off error (iii) representation of zero as floating point number (iv) significant digits in a decimal number representation (v) normalized representation of a floating point number (vi) overflow
Express A³f, as a backward difference.
Compute the value of the integral
by using
Rectangular Rule (ii) Trapezoidal Rule and then (iii) Simpson's 1/3 Rule
Obtain Approximate the value of (3.7)-1 using first three terms of Taylor's series expansion.
Calculate a bound for the truncation error in approximating
where
and (fact n) denotes factorial of n