15 Fixed and Floating-Point arithmetic

Question 1

Fixed point numbers?

Answer 1

Question 2

Binary fixed point numbers?

Answer 2

Question 3

What is the decimal representation of 1101.101?

Answer 3

13.625

Question 4

There are two ways of representing signed numbers:

Answer 4

1) sign/magnitude notation
2) two‘s complement notation

Question 5

What is the fixed point representation of -2.375?

Answer 5

Question 6

Arithmetic with fixed point numbers

Compute the following: 0.75 + (-0.625)

Answer 6

Question 7

How are Fixed point numbers represented in a computer?

Answer 7

Question 8

8 bit fixed point number range?

Answer 8

Range of values with 8 bits: +7.9375, -7.9375

Question 9

Why do we need floating point numbers?

Answer 9

Question 10

The normal scientific notation is of the form for floating point integers?

Answer 10

The number 4.1x10³ , which is the decimal scientific notation of 41000, has positive sign, mantissa of 4.1, base of 10 and exponent of 3. Here the decimal point floats to the position right after the most significant bit.

Question 11

In binary floating point representation, the mantissa is composed of 0s and 1s, and the base is always 2.

Answer 11

Question 12

8 bit Floating point numbers represented in a computer

Answer 12

Question 13

How do we store a 8 bit floating point number with a negative exponent?

Answer 13

Question 14

Answer 14

Question 15

Formula to obtained the bias number?

Answer 15

Question 16

Answer 16

Question 17

Adding the bias to the exponent, we get the 32-bit representation defined by the IEEE 754 floating point standard.

Answer 17

Question 18

The Floating point range with the 32 and 64bit IEEE 754 standard?

Answer 18

Question 19

IEEE standard special cases?

Answer 19

Question 20

Rounding options?

Answer 20

There are a range of options when considering how to round an arithmetic result • Down • Up • Nearest (Default)

Question 21

Overflowing and underflowing

Answer 21

A value that gets to large Overflows and is set to + or - infinity if it is to large a negative number A value that is too small Underflows and is set to zero

Question 22

The steps for adding floating-point numbers with the same sign are as follows:

Answer 22

1. Extract exponent and fraction bits.
2. Prepend leading 1 to form the mantissa.
3. Compare exponents.
4. Shift smaller mantissa if necessary.
5. Add mantissas.
6. Normalize mantissa and adjust exponent if necessary.
7. Round result.
8. Assemble exponent and fraction back into floatingpoint number.