floating point

Question 1

Converting from FP to denary?

Answer 1

• Convert exponent to denary.
• If its negative move binary point left (adding 1’s if mantissa is negative and 0’s if its +ve)
• If its positive move binary point right
• Convert New mantisa.

Question 2

Converting from twos comp to binary?

Answer 2

starting from the right, leave every bit until the first 1. Then flip all the bits after this 1.

Question 3

Converting from denary to FP?

Answer 3

• Convert to Binary
• Twos completment this
• Figure out how much you need to move the BP to get normalised form?
• Create the exponent of this number (with correct sign, negative number was a fraction, +ve number was >1)

Question 4

What is the normalised form?

Answer 4

• Positive starts with 0.1
• Negative Starts with 1.0

Question 5

WHy is normalised form good?

Answer 5

• Maximises precision for given number of bits
• Unique representation of each number

Question 6

Why is fixed point used?

Answer 6

As it has a larger randge of number in the same number of bits as fixed point representation.

Question 7

What does storing something in excess 127 mode mean?

Answer 7

that 127 was added to the exponent before it was stored.

Question 8

LArgest positive number?

Answer 8

Matissa : 0.11111 etc

Exponent 01111 etc

Question 9

Smallest positive number

Answer 9

mantissa : 0.1000000 etc

exponent: 10000000 etc

Question 10

Largest negative number

Answer 10

mantissa : 1.0000000 etc

exponent: 0111111111 etc

Question 11

smallest negative number

Answer 11

mantissa : 1.0111111 etc

exponent: 100000 etc

Question 12

Two tpes of rounding error?

Answer 12

• Absolute error
• Relative error

Question 13

What is the relative error?

Answer 13

The absolute erro divited by the required value

Question 14

what is the absolute error?

Answer 14

The differenc ebetween the actual number and the nearest representable value

Question 15

What is presision?

Answer 15

the maximum numbe rof significant digits that can be represented.

(determined by mantissas bits)

Question 16

What does increasing mantissa size, and decreasing exponent bits do?

Answer 16

More pression less range

Question 17

what does decreasing mantissa bits, and increasing exponent bits do?

Answer 17

Decreases precision, Increases range

Question 18

what is a cancelation error?

Answer 18

Adding a small number to a very large number has no effect, as the number of bits storing the mantissa cant record the difference.

Question 19

What is underflow?

Answer 19

Where the result of the calculation is too small to be represented in the avalable number of bits, will be stored as 0. Eg dividing a very small number

Question 20

What is overflow?

Answer 20

The reult of a calulation is too large to be represented with the avalable bits.

eg multiplying two large numbers.