Lecture 6: Decimal Real Numbers

Question 1

Name two ways to represent decimal real numbers in for computing purposes.

Answer 1

Fixed point binary and IEEE 754 standard.

Question 2

Explain exponent-mantissa format and normalised form.

Answer 2

Having a mantissa multiplied by an exponent and normalised form is the same but explicitly with only one non-zero digit to the left of decimal point.

Question 3

What are hte drawbacks of fixed-point binary?

Answer 3

Uses up lots of bits.

Question 4

How is the 32-bit IEE standard broken up?

Answer 4

• 1-bit sign for mantissa
• 8-bit exponent
• 23-bit mantissa

Question 5

What notation is used for storing exponent? Explain it.

Answer 5

Excess 127.
E.g. 130. 130-127 = 3. Exponent is 3.
125. 125-127 = -2. Exponent is -2.

Question 6

For excess 127 notation, what do 0 and 255 represent?

Answer 6

0, infinity and NaN, respectively. Infinity and NaN are both exponent 255 but infinity is mantissa = 0 and NaN is any non zero number.