4.5.4 FoDR - Binary Number System

Question 1

What is the difference between unsigned and signed binary

Answer 1

• Unsigned binary can only be used to represent Natural numbers, Whereas signed binary is used to represent Integer numbers

Question 2

What is the minimum value that can be represented in unsigned binary with n bits

Answer 2

0

Question 3

What is the maximum value that can be represented in unsigned binary with n bits

Answer 3

2ⁿ-1

Question 4

What is meant by an overflow

Answer 4

Where the result of an operation has more bits than there are available

Question 5

What is meant by an underflow

Answer 5

Where the result of an operation has less bits than there are available

Question 6

What is the range for the number of numbers that you can represent using the Two’s complement

Answer 6

-2ⁿ –> 2ⁿ⁻¹-1

Question 7

How many numbers can be represented using twos complement

Answer 7

2ⁿ

Question 8

What are the advantages of Fixed Point

Answer 8

• Simpler to calculate therefore the process is generally faster

Question 9

What are the advantages of Floating Point

Answer 9

• Has a larger range for the same number of bits

Question 10

What are the characteristics of Floating Point Binary

Answer 10

• Uses Mantissa and Exponent
• Precision depends on the number of bits used to represent the mantissa
• Range depends on the number of bits used to represent th eexponent

Question 11

What are the characteristics of Fixed Point Binary

Answer 11

• The range depends on how close the binary point is to the LSB
• The precision depends on how close the binary point is to the MSB

Question 12

Why can both representation of fractional binary be inaccurate

Answer 12

Some numbers can just not be represented exactly in binary, this means it can only be an approximation e.g. 0.1, which can cause rounding errors

Question 13

How do you round a binary number

Answer 13

• Look at the first bit that you cannot store
• If its a 1, add 1 to the whole number, then truncate the number
• If 0, truncate the number

Question 14

What are the conditions for binary number to be normalised

Answer 14

• If positive: 0.1
• If negative: 1.0

Question 15

What is the condition for a real number to be represented in a binary number system

Answer 15

Its fractional part must be able to be represented exactly in binary

Question 16

What is meant by the absolute error

Answer 16

The difference between the approximation and the true value

Question 17

What is the equation for the absolute error

Answer 17

A = difference between true value and approximation

Question 18

What is meant by the relative error

Answer 18

A measure of the uncertainty in a given value compared to the true value

Question 19

What is the equation for relative error

Answer 19

Relative Error = Absolute Error/ Actual Value