Some Sort of Review Session

We started with number representation.

• Significance is the value of each number based on their position.
  • Arithmetic operations incur error due to loss of significance.
  • Absolute error: |X - X_s|
  • Relative error: \frac{|X - X_s|}{X} (accounts for magnitude)
• Know integers to binary.
• Know non-integers to binary (same, except we do successive multiplication / inverse multiplication).
• Know scientific notation.
• Know IEEE-754 standard.
  • Know 32-bit and 64-bit.
  • Know range is [126, 127] (account for bias and special signals)
• Know machine epsilon (smallest number such that when it’s added to one
  • IEEE 754: 2^-23

Practice:

• Convert 42 to binary
  • And back
• Convert 1.25 to floating-point binary
  • And back
• Convert 1.25 to IEEE-754
  • And back

Linear System: Set of n equations consisting of a combination of n variables.

• Know Naive Gaussian Elimination
• Know Scaled Partial Pivoting
  • We’ll do this one on the test.
  • Remember do solve like a human (don’t do programming stuff like make a swap vector)

Calculator Apps: Professor allows calculator programming.

• SPP Aid: I can do the steps, I just need to simplify data entry, because I’m really bad at typing.
• Decimal -> Binary (must handle floating point, e.g. 1101.01)
  • Needs to provide a table for successive division/multiplication
  • Backwards, too?
• Notes on IEEE-754 standard cheat sheet.