1.4 Data Representation and Data Types

Question 1

What is a bit? (2)

Answer 1

1. A single “1” or “0”
2. Is the smallest unit of data.

Question 2

What is a byte?

Answer 2

A sequence of 8 bits.

Question 3

What is a word? (2)

Answer 3

1. The number of bits that can be simultaneously processed or stored in a single register.
2. Different for different computers

Question 4

How many bits are there in a word?

Answer 4

It is usually 32 or 64 bit.

Question 5

What is the binary number system?

Answer 5

1. It stores data via an arrangement of 1 and 0.
2. It is a base 2 system.

Question 6

What is hexadecimal? (2)

Answer 6

1. A way of writing binary using letters and numbers.
2. It is a base 16 system.

Question 7

How can hexadecimal be used as shorthand?

Answer 7

The binary number can be split into groups containing 4 digits/bits and represented by a number.

Question 8

What are the advantages of using
hexadecimal?

Answer 8

Fewer errors will occur as it is easy to read a large binary number.

Question 9

What are character sets?

Answer 9

A list of characters alongside corresponding binary codes.

Question 10

How do character sets work?

Answer 10

When a computer stores text, it stores a sequence of binary codes, and two computers that use the same character set can communicate with one another.

Question 11

Give 2 character sets.

Answer 11

1. ASCII
2. Unicode

Question 12

How does ASCII store characters?

Answer 12

It stores characters that can be found on standard UK keyboards using 7bits per character.

Question 13

How does Unicode store characters?

Answer 13

It stores a huge range of characters from many languages, as well as emoticons and other symbols, using 16 bits per character.

Question 14

Give an advantage for ASCII.

Answer 14

Very little storage space required per character.

Question 15

Give a disadvantage for ASCII.

Answer 15

Limited to using western characters only.

Question 16

Give 2 advantages for Unicode.

Answer 16

1. Many more characters can be used.
2. Possibility to store more in the future.

Question 17

Give a disadvantage for Unicode.

Answer 17

Requires more than double the storage space per character of ASCII.

Question 18

What is a primitive data type? (2)

Answer 18

1. A primitive data type is a data type that cannot be broken down into smaller data types.
2. A variables data type determines what can be stored in that variable.

Question 19

What is a variable?

Answer 19

A named space in memory that can contain one piece of data of a specified data type.

Question 20

State 5 data types.

Answer 20

1. Boolean
2. Character
3. String
4. Integer
5. Real

Question 21

What is a Boolean?

Answer 21

Can only be True or False.

Question 22

What are the storage requirements of a Boolean?

Answer 22

1 bit

Question 23

What is a Character?

Answer 23

Stores content of a single keystroke.

Question 24

What are the storage requirements of a
Character? (2)

Answer 24

1. For ASCII : 7 bit
2. For Unicode : 16 bit

Question 25

What is a String?

Answer 25

A sequence of characters.

Question 26

What are the storage requirements of a string?

Answer 26

Number of characters in string, 7 (if ASCII) or 16 (if Unicode).

Question 27

What is an Integer?

Answer 27

Whole numbers including positives, negatives and zero.

Question 28

What are the storage requirements of an Integer?

Answer 28

Variable - longer it is the more bits needed.

Question 29

What is a Real?

Answer 29

Numbers that can contain fractions and decimal points.

Question 30

What are the storage requirements of a Real?

Answer 30

Variable - More bits allow storage of larger numbers and more precise fractions.

Question 31

What is an arithmetic shift to the right of n places?

Answer 31

Equivalent of dividing by 2^n.

Question 32

What is the difference between an arithmetic shift and a logical shift?

Answer 32

An arithmetic shift maintains details with the sign bit. A logical shift does not.

Question 33

What are the two ways an integer can be stored in fixed length?

Answer 33

1. Sign and Magnitude 2. Two’s Compliment

Question 34

What is sign and magnitude? (2)

Answer 34

1. The first bit in the sequence is a sign bit and has no numerical value. 2. 0 : positive, 1 : negative

Question 35

What does the placeholder for sign and magnitude look like?

Answer 35

(-) 64 32 16 8 4 2 1

Question 36

What is Two’s Compliment?

Answer 36

The left most bit is negative.

Question 37

What does the placeholder for Two's Compliment look like?

Answer 37

-128 64 32 16 8 4 2 1

Question 38

What is a way to store an unfixed length?

Answer 38

Unsigned fixed points.

Question 39

What is the placeholder for an unsigned fixed point with the point after 4 bits?

Answer 39

8 4 2 1 .5 .25 .125 .0625

Question 40

What is another way in which a computer stores numbers?

Answer 40

Floating point form

Question 41

What is floating point form? (2)

Answer 41

1. It is the binary equivalent to standard form. 2. It consists of a Mantissa and an Exponent (M x 2ᴱ).

Question 42

State 2 advantages of using integer form to store numbers.

Answer 42

1. For small values, data stored in this format required less storage space. 2. There is no overhead - no need to calculate the values before processing it.

Question 43

State 2 disadvantages of using integer form to store numbers.

Answer 43

1. Fractions can not be stored. 2. For an extremely large number (eg Trillion) an integer would require far more storage space than floating point.

Question 44

State 3 advantages of using floating point form to store numbers.

Answer 44

1. Fractions can be stored. 2. Extremely large numbers require fewer bits to store compared to integer form. 3. Can store numbers completely precisely/ accurately

Question 45

State 2 disadvantages of using floating point form to store numbers.

Answer 45

1. For small integer values (eg 32) more bits are used than would be in integer form 2. There is an overhead – processor time is needed to calculate the value stored before it can be processed.

Question 46

State 2 ways to approximate numeric data.

Answer 46

1. Truncation 2. Rounding

Question 47

What does rounding do?

Answer 47

It takes a number to the nearest integer or (in binary) the nearest half, quarter, eighth.

Question 48

Give an example of rounding.

Answer 48

7.8 ----> 8

Question 49

What does truncation do?

Answer 49

It disregards values after a certain number of digits relative to the binary (or decimal) point.

Question 50

Give an example of truncation.

Answer 50

7.8 ----> 7

Question 51

Why is rounding generally more appropriate than truncation?

Answer 51

Rounding tends to give answers nearer to the original number.

Question 52

State 3 errors caused by rounding and truncation.

Answer 52

1. A continued use in further calculation increases inaccuracy. 2. A test for equality might fail if a minor difference is caused by rounding. 3. In some applications a high accuracy is vital and rounding may reduce this accuracy.

Question 53

When does an underflow occur?

Answer 53

When a number is very close to zero to be stored by the computer.

Question 54

When does an overflow occur?

Answer 54

When a number is too large to be stored by a computer.