1. a. Find the binary expression of - Show your calculations. 1. =-+ 1 + 128 1 b. Show that the binary expression from part a is equivalent to 16 256 c. How big of an error can be expected in computing E° 000 using a 64-bit computer. 2. Use the mantissa table and calculate (+) +. 10 3. Given that f,4e*´dx = 0.2553074606. Determine the accuracy of the approximation obtained by replacing the integrand by Taylor polynomial series with the first four terms. a. State what type of error is present in this situation. b. Compute the significant digits. 1-cosx 4. Let f(x) What drawback could there be in using this formula to obtain values sin x of the function? a. Specify the range of x values for which this drawback exists. b. Introduce an alternative way of accurately computing the function for those x values. 5. Given Taylor polynomial expansions: 1 = 1 + h + h² + h3 + h* + 0(h5) 1 - h h? h3 In(1+h) = h - 2+3 + 0(h*) | Determine the order of approximation for their sum and product.
1. a. Find the binary expression of - Show your calculations. 1. =-+ 1 + 128 1 b. Show that the binary expression from part a is equivalent to 16 256 c. How big of an error can be expected in computing E° 000 using a 64-bit computer. 2. Use the mantissa table and calculate (+) +. 10 3. Given that f,4e*´dx = 0.2553074606. Determine the accuracy of the approximation obtained by replacing the integrand by Taylor polynomial series with the first four terms. a. State what type of error is present in this situation. b. Compute the significant digits. 1-cosx 4. Let f(x) What drawback could there be in using this formula to obtain values sin x of the function? a. Specify the range of x values for which this drawback exists. b. Introduce an alternative way of accurately computing the function for those x values. 5. Given Taylor polynomial expansions: 1 = 1 + h + h² + h3 + h* + 0(h5) 1 - h h? h3 In(1+h) = h - 2+3 + 0(h*) | Determine the order of approximation for their sum and product.
Chapter22: Sequence Control
Section: Chapter Questions
Problem 6SQ: Draw a symbol for a solid-state logic element AND.
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Transcribed Image Text:1. a. Find the binary expression of - Show your calculations.
1..
b. Show that the binary expression from part a is equivalent to =+-+p+
1
8
16
128
256
c. How big of an error can be expected in computing E"
000 = using a 64-bit computer.
2. Use the mantissa table and calculate (+) +.
3. Given that ſ,4 e*
´dx = 0.2553074606. Determine the accuracy of the approximation
obtained by replacing the integrand by Taylor polynomial series with the first four terms.
a. State what type of error is present in this situation.
b. Compute the significant digits.
1-cosx
4. Let f(x)
What drawback could there be in using this formula to obtain values
sin x
of the function?
a. Specify the range of x values for which this drawback exists.
b. Introduce an alternative way of accurately computing the function for those x values.
5. Given Taylor polynomial expansions:
1
= 1+h + h² +h³ + h* + 0(h5)
1-h
h? h3
In(1+ h) = h –+
+ 0(h*)
2
Determine the order of approximation for their sum and product.
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