Binary number systems

Question 1

Steps to normalise with a positive mantissa, positive exponent.

Answer 1

shift right for positive exponent

Question 2

Steps to normalise with a positive mantissa, negative exponent.

Answer 2

shift left for negative exponent

Question 3

Steps to normalise with a negative mantissa, positive exponent.

Answer 3

Complete two’s complement, then shift right for positive exponent

Question 4

Steps to normalise with a negative mantissa, negative exponent.

Answer 4

Complete two’s complement on the number, then shift left for negative exponent

Question 5

What is the difference between signed and unsigned Binary?

Answer 5

Signed Binary can represent positive and negative numbers whereas unsigned binary only represents positive numbers

Question 6

What is an advantage of using unsigned binary?

Answer 6

Unsigned Binary can store larger numbers

Question 7

What does rounding do?

Answer 7

Rounding is necessary when we can’t represent a number however it creates an error as it’s not as accurate.

Question 8

What are the two types of errors?

Answer 8

Absolute and Relative

Question 9

How do we calculate Absolute error?

Answer 9

Real value - Stored value

Question 10

How do we calculate Relative error?

Answer 10

Exact value - Stored value / Exact value
or
Absolute Error / Exact value

Question 11

What is precision?

Answer 11

Precision is to do with word length and the maximum number of significant digits that can be represented

Question 12

What is Range?

Answer 12

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

Question 13

What is floating point?

Answer 13

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

Question 14

What is fixed point?

Answer 14

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

Question 15

What’s an advantage of Fixed point over Floating point?

Answer 15

• Fixed point binary has more precision than floating point

- Used when a high level of precision and speed is needed

Question 16

What’s an advantage of Floating point over Fixed point?

Answer 16

Floating point can represent a wider range of numbers that fixed point
- Used when a wide range of values needs to be represented

Question 17

What is normalised floating point?

Answer 17

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

Question 18

What is Underflow ?

Answer 18

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

Question 19

What is Overflow ?

Answer 19

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

Question 20

How do you calculate the range of an unsigned binary bit pattern?

Answer 20

2^n = the amount of numbers that can be represented, then 0 to (2^n -1) is the range

Question 21

How do you calculate the range of an signed binary bit pattern?

Answer 21

-(2^(n-1)) to (2^(n-1)-1)