Binary

Question 1

Define unsigned binary:

Answer 1

Binary that only represents positive numbers

Question 2

0+0:

Answer 2

0

Question 3

0+1:

Answer 3

1

Question 4

1+1:

Answer 4

0, carry 1

Question 5

1+1+1:

Answer 5

1, carry 1

Question 6

Binary multiplication rules:

Answer 6

Multiply the first number by each digit of the second, shifting one left each time. Each result will be 0 or the original number shifted by an appropriate amount. Then add all the results.

Question 7

Define two’s complement:

Answer 7

A method of working with signed binary values

Question 8

How does two’s complement work:

Answer 8

The most significant bit is negative, the rest are positive.

Question 9

How to convert positive numbers to negative ones:

Answer 9

Flip all the digits, then add 1

Question 10

Binary subtraction rules:

Answer 10

Convert the number being subtracted into a negative number, then add them

Question 11

Define fixed point:

Answer 11

Where the decimal point is in a fixed position in a number

Question 12

Where is the decimal point in a fixed point number:

Answer 12

It can be anywhere, it just can’t move so the size of the number is limited by where it is

Question 13

Define floating point:

Answer 13

Where the decimal point can move within a number

Question 14

What is the benefit of floating point numbers:

Answer 14

It means less bits are needed, and that a wider range of numbers is available

Question 15

Define mantissa:

Answer 15

The actual number being represented in floating point, not to the actual power

Question 16

Define exponent:

Answer 16

What power the mantissa is raised to to give the actual number

Question 17

If the exponent is positive, what happens to the point:

Answer 17

The point shifts left - the mantissa increases in size

Question 18

If the exponent is negative, what happens to the point:

Answer 18

The point shifts right - the mantissa becomes smaller

Question 19

Where is the decimal point in a normalised floating point number:

Answer 19

After the most significant bit of the mantissa

Question 20

What are floating point numbers equivalent to in decimal:

Answer 20

Standard form

Question 21

What is the benefit of fixed point numbers:

Answer 21

Less processing is required, so it’s faster and the absolute error is always the same

Question 22

Define signed binary:

Answer 22

Binary that can represent positive and negative numbers

Question 23

Define overflow error:

Answer 23

When a number is too big to be represented with the allocated number of bits

Question 24

Define underflow error:

Answer 24

When a number is too small to be represented with the allocated number of bits

Question 25

Define precision:

Answer 25

How accurate a number is

Question 26

Define normalisation:

Answer 26

A process for adjusting numbers onto a common scale

Question 27

How much is a positive number adjusted to be normalised:

Answer 27

It should have a 0 as the most significant bit, and a 1 after it

Question 28

How much is a negative number adjusted to be normalised:

Answer 28

It should have a 1 as the most significant bit, and a 0 after it

Question 29

Define rounding error:

Answer 29

When the actual number can’t be represented in the available number of bits or at all (like 1/3), so it is up to the programmer to decide how accurate it needs to be

Question 30

Define absolute error:

Answer 30

The error interval between the actual number and the number being used

Question 31

How to calculate the absolute error:

Answer 31

The smaller number subtracted from the larger number (it’s always positive)

Question 32

Define relative error:

Answer 32

The comparative error between the number and how accurate it needs to be

Question 33

How to calculate the relative error:

Answer 33

The absolute error divided by the actual number

Question 34

Where is the point in a normalised number:

Answer 34

After the MSB