Notebook 4

Question 1

Number

Answer 1

String of digits in a base b

Question 2

Bits

Answer 2

Binary Digits

Question 3

Floating Point Storage

Answer 3

Encode numbers with fractional parts in a systematic way using fixed-size encoding.

Question 4

Systematic encoding

Answer 4

sign, significand, exponent

Question 5

Systematic encoding

Answer 5

sign, significand, exponent

Question 6

Rounding Error

Answer 6

Not being able to store the exact solution due to too much digits

Question 7

Binary Encoding

Answer 7

IEEE 754 Standard

Question 8

IEEE Double-precision

Answer 8

64 bits total
1 sign bit
53 bit significant
11 bit exponent

Question 9

IEEE Single-precision

Answer 9

32 bits total
1 sign bit
24 bit significand
8 bit exponent

Question 10

Analyzing Floating-point programs

Answer 10

f(x) = Function to compute
alg(x) = program to compute f(x)
lalg(x)- f(x)l - forward stability analysis

Question 11

“small”

Answer 11

forward stable

Question 12

Forward Stable

Answer 12

|alg(x) - f(x)| <= “small”

Question 13

Backward Stable

Answer 13

alg(x) = f(x+deltax),|deltax|

Question 14

Taylor’s theorem

Answer 14

f(x+deltax) = f(x) + deltax x first deriv x

Question 15

Small backward error ->

Answer 15

forward error small