Topic 5 - Rounding Errors

Question 1

What is a rounding error?

Answer 1

When rounding creates an error between the original number and the rounded number

Question 2

Define absolute error

Answer 2

Absolute error is the difference between the theoretical exact value calculated with no errors present and the processed computed value to be stored

Question 3

Define relative error

Answer 3

Relative error is the value of the absolute error divided by the theoretical exact value with no errors present

Question 4

What is the formula to find absolute error

Answer 4

MOD (exact value - computed value)

Question 5

What is the formula to find the relative error

Answer 5

exact value

Question 6

Find absolute and relative errors for a computed value of 0.02 and an exact value of 0.017.

Answer 6

Absolute error = MOD (exact value - computed value)
Absolute error = MOD (0.017-0.02) = 0.003

Relative error = Absolute error over exact value
Relative error = 0.003/0.017 = 0.17647

Question 7

Define precision

Answer 7

Precision is associated with word length and the maximum number of significant digits that can be represent

Question 8

Define range

Answer 8

range is the set of all numbers that can be represented using a specific number system

Question 9

Define floating point

Answer 9

Floating point is a real data type where the binary point can move within the number

Question 10

Define fixed point

Answer 10

Fixed point is a real data type where a number has a fixed number of digits either before or after the decimal point

Question 11

Define normalised floating point

Answer 11

Normalised floating point number is where the binary point position is fixed in standard form position and the exponent can float to reflect different values of that number

Question 12

Define mantissa

Answer 12

Mantissa is the part of the floating point number that includes the significant digits within a number

Question 13

Define exponent

Answer 13

Exponent is the power that the number within the mantissa is raised

Question 14

Define underflow

Answer 14

If the result of a calculation is smaller than the smallest number that can be represented by the system, then an underflow will occur and the result will be stored as zero; dividing very small numbers can cause underflow.

Question 15

Define overflow

Answer 15

If the result of a calculation is too large a value to be represented by the system, then an overflow will occur; this can cause serious problems and is most likely to occur when multiplying two large numbers. Double precision registers can be used to minimise the occurrence of overflow.

Question 16

When does underflow occur?

Answer 16

Underflow occurs where the required value is too small to be stored using the number of bits available

Question 17

When does overflow occur?

Answer 17

Overflow occurs where the required value is too large to be stored using the number of bits available