Data Representation 1

Question 1

What is a Bit?

Answer 1

0 or 1, binary digit

Question 2

What is a byte?

Answer 2

8 bits

Question 3

What is a Natural number ?

Answer 3

ℕ Positive whole numbers

{0,1,2,3,4…}

Question 4

What is an Integer number?

Answer 4

ℤ Whole numbers (positive or negative)

{…,-3,-2,-1,0,1,2,3,…}

Question 5

What is a Rational number?

Answer 5

ℚ Numbers can also be expressed as fractions (ratios of integers)
{…, -42, -1/1, -1/3, -1/2, 0, 1/2, 1/3, 1/1, 7, …}

Question 6

What is an Irrational number?

Answer 6

Numbers cannot be expressed as a fraction. Examples include π (Pi), √2, e (Euler’s number)

Question 7

What is ℕ?

Answer 7

Natural numbers

Question 8

What is ℤ?

Answer 8

Integer numbers

Question 9

What is ℚ?

Answer 9

Rational number

Question 10

What is a Real number?

Answer 10

ℝ Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.

Question 11

7 is what type of number (it is more than one)

Answer 11

ℕ (natural), ℤ (integer), ℚ (rational) and ℝ (real)

Question 12

What is ℝ?

Answer 12

Real numbers

Question 13

-9 is what type of number (it is more than one)

Answer 13

ℤ (integer), ℚ (rational) and ℝ (real)

Question 14

1/3 is what type of number (it is more than one)

Answer 14

ℚ (rational) and ℝ (real)

Question 15

-10/11 is what type of number (it is more than one)

Answer 15

ℚ (rational) and ℝ (real)

Question 16

π (Pi) is what type of number (it is more than one)

Answer 16

irrational and ℝ (real)

Question 17

What is an ordinal number?

Answer 17

Ordinal numbers indicate the positions of the values 1st, 2nd, 3rd…

Question 18

What base is binary?

Answer 18

Base 2 (0 or 1)

Question 19

What base is decimal/denary?

Answer 19

Base 10 (0,1,2,3,4,5,6,7,8,9)

Question 20

What base is hexadecimal?

Answer 20

Base 16 (0 to 9 and A,B,C,D,E,F)

Question 21

How many different values can be represented with n bits?

Answer 21

2^n

Question 22

How many different values can be represented with 3 bits?

Answer 22

2^3 = 8 different values (000,001,010,011,100,101,110,111)

Question 23

How many different values can be represented with 8 bits?

Answer 23

2^8 = 256

Question 24

What is Unsigned binary?

Answer 24

Unsigned binary integers are numbers without any ‘+’or ‘-‘ sign.

Question 25

What is signed binary?

Answer 25

Signed binary numbers means that both positive and negative numbers may be represented.

Question 26

What is two's complement?

Answer 26

A method of representing signed binary where the MSB (most significant bit is negative). For example with 4 bits the column headings would be -8 | 4 | 2 | 1

Question 27

Unsigned binary value 101 in denary

Answer 27

5

Question 28

Signed binary value 101 in denary

Answer 28

-3

Question 29

Signed binary value 0101 in denary

Answer 29

5

Question 30

Hexadecimal value E in denary

Answer 30

14

Question 31

Hexadecimal value 1A in denary

Answer 31

26

Question 32

Hexadecimal value 20 in denary

Answer 32

32

Question 33

Hexadecimal C in binary

Answer 33

1100

Question 34

Hexadecimal D4 in binary

Answer 34

1101 0100

Question 35

Binary 11110111 to Hexadecimal

Answer 35

F7

Question 36

Binary 01101011 to Hexadecimal

Answer 36

6B

Question 37

A kilobyte is...

Answer 37

1000 bytes / 10^3 bytes

Question 38

A kibibyte is...

Answer 38

1024 bytes / 2^10 bytes

Question 39

``` Give the symbols and corresponding powers of 2 for the binary prefixes: kibi mebi gibi tebi ```

Answer 39

kibi, Ki - 2^10 mebi, Mi - 2^20 gibi, Gi - 2^30 tebi, Ti - 2^40

Question 40

``` Give the symbols and corresponding powers of 10 for the decimal prefixes: kilo mega giga tera ```

Answer 40

kilo, k - 10^3 mega, M - 10^6 giga, G - 10^9 tera, T - 10^12

Question 41

Unsigned binary: Give minimum and maximum values for 4 bits.

Answer 41

0 to 15 | 0 to 2^4 - 1

Question 42

Unsigned binary: Give minimum and maximum values for 8 bits.

Answer 42

0 to 255 | 0 to 2^8 - 1

Question 43

Binary addition 1 + 1?

Answer 43

10

Question 44

Binary addition 1 + 0?

Answer 44

1

Question 45

Binary addition 1 + 1 + 1?

Answer 45

11

Question 46

Binary multiplication 1 * 0?

Answer 46

0

Question 47

Binary multiplication 1 * 1?

Answer 47

1

Question 48

Binary multiplication 10 * 1?

Answer 48

10

Question 49

Binary multiplication 101 * 10?

Answer 49

1010

Question 50

Binary multiplication 111 * 11?

Answer 50

1110

Question 51

Fixed point binary, give the decimal value of 011.100

Answer 51

3.5

Question 52

Fixed point binary, give the decimal value of 0.001

Answer 52

1/8

Question 53

Fixed point binary in two's complement, give the decimal value of 111.100

Answer 53

-1/2

Question 54

Rounding error

Answer 54

For a real number to be represented exactly by the binary number system, it must be capable of being represented by a binary fraction in the given number of bits. Some values cannot ever be represented exactly, for example 1/10.

Question 55

Floating point binary the number is divided in two parts, name them:

Answer 55

Mantissa and Exponent

Question 56

The mantissa is...

Answer 56

The part of a floating-point number which represents the significant digits of that number.

Question 57

The exponent is...

Answer 57

The part of a floating-point number used as a multiplier to move the mantissa to the correct 'size', so increasing its storage size results in a larger range of possible numbers.

Question 58

A positive floating-point number starts with...

Answer 58

0.1

Question 59

A negative floating-point number starts with...

Answer 59

1.0

Question 60

Both mantissa and exponent are stored using what?

Answer 60

Two's Complement

Question 61

What is the absolute error?

Answer 61

The difference between the number you are trying the store and the nearest value that you can.

Question 62

What is the relative error?

Answer 62

The relative error is the absolute error divided by the actual value. Often displayed as a percentage.