Section 3 - Data Representation - Part 1

Question 1

What is a natural number?

Answer 1

A whole number that is used in counting

Question 2

What is a rational number?

Answer 2

Any value that can be expressed as a ration or fraction

Question 3

What is an irrational number?

Answer 3

A value that cannot be expressed as a fraction and has an endless series of repeating digits

Question 4

What is a real number?

Answer 4

A real number is any natural, rational or irrational number. It is the set of all possible real world quantities

Question 5

What are ordinal numbers?

Answer 5

Numbers that describe the numerical position of objects

Question 6

What base is decimal?

Answer 6

10, with digits 0 - 9

Question 7

What base is hexadecimal?

Answer 7

16, with digits 0 - 9 and A - F

Question 8

What base is binary

Answer 8

2, with digits 0 and 1

Question 9

How do you convert from binary to hex?

Answer 9

Split the binary number into groups of 4 binary digits and convert each group to their hex equivalent

Question 10

How do you convert from hex to binary?

Answer 10

Convert each hex digit into the equivalent value with 4 binary digits

Question 11

How do you convert from hex to decimal?

Answer 11

Multiply the left column by 16 and the right column by 1, then sum the results

Question 12

How do you convert from decimal to hex?

Answer 12

Convert the decimal number to binary, then the binary into hex

Question 13

Why is hex used?

Answer 13

• Fewer mistakes will be made when copying the value as it is shorter
• It is easier to remember

Question 14

What is a bit?

Answer 14

A fundamental unit of information, either a single 1 or 0. They are used to represent the 2 electronic states (on and off)

Question 15

What is a byte?

Answer 15

A set of 8 bits

Question 16

What is a nibble?

Answer 16

A set of 4 bits

Question 17

What is the number of values that can be represented by n bits?

Answer 17

2^n

Question 18

What is ASCII code?

Answer 18

Previously it was the standard code for representing the characters on the keyboard. It uses 7 bits, forming 128 different bit combinations which is more than enough to cover all the characters on a standard English-Language keyboard

Question 19

Why can ASCII not be used for arithmetic?

Answer 19

The number character is not the same as the actual number value. For example the ASCII value for 7 is 0110111 which is actually 55 in binary

Question 20

How many bits are there in ASCII code?

Answer 20

Originally ASCII code used 7 bits, however an 8-bit version was developed to include an additional 128 combinations to represent symbols

Question 21

What is unicode?

Answer 21

The global standard for multilingual data. There are 16 and 32 bit variations. It is compatible with ASCII because the first 128 codes are the sameW

Question 22

What is the downside of unicode?

Answer 22

Unicode encodings take more storage space, increasing file size and transmission times

Question 23

What is error checking?

Answer 23

A variety of systems used to verify that the data they receive is actually the same as the data that was sent

Question 24

Why do computer systems use error checking?

Answer 24

Bits can change during transmission due to interference

Question 25

What are parity bits?

Answer 25

An additional bit used to check that the other bits transmitted are likely to be correct. Computers use either odd or even parity

Question 26

What is majority voting?

Answer 26

A system that requires each bit to be sent 3 times. If a bit value is flipped erroneously during transmission over a noisy line, the recipient computer would use the majority rule and assume that the 2 bits that have not changed were therefore correct.

Question 27

What are checksums?

Answer 27

A mathematical algorithm that is applied to a packet of data. The data in the block is used to create a checksum value which is transmitted alongside the block. The same algorithm is applied to the block after transmission and if the 2 checksum match then the transmission is considered successful. If they do not match then the block is transmitted again

Question 28

What are check digits?

Answer 28

An additional digit at the end of a string of other numbers designed to check for mistakes in input or transmission

Question 29

What check digits do books use?

Answer 29

They have a unique ISBN or EAN. The first 12 digits are the unique item number and the 13th number is the check digit. It can be calculated using the Modulo 10 system

Question 30

When does an overflow error occur in binary addition?

Answer 30

Where a carry from the most significant bit requires another bit

Question 31

What is the difference between signed and unsigned binary numbers?

Answer 31

A signed representation can represent both positive and negative numbers, unsigned representation of binary numbers can only represent positive numbers

Question 32

What is two's complement?

Answer 32

A representation of a signed binary number

Question 33

How can you work out the range that can be represented by two's compliment?

Answer 33

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

Question 34

How can you convert a negative decimal number to binary?

Answer 34

Work out the positive equivalent of the number, then flip all the bits and add 1

Question 35

How can you convert a negative binary number to decimal?

Answer 35

Flip all the bits and add 1 before converting the binary number as usual

Question 36

How can you do subtraction with two's complement?

Answer 36

By converting the negative number to it's two's complement form and adding both numbers, ignoring any carry on

Question 37

What are fixed point binary numbers used for?

Answer 37

To represent fractions in binary, with a binary point used to separate the whole place values from the fractional part

Question 38

How can you convert a decimal fraction to fixed point binary?

Answer 38

You use the same technique when converting any number into binary

Question 39

What are the issues with fixed point binary?

Answer 39

- Some fractions cannot be represented at all due to requiring an infinite number of bits to the right of the point. This will result in truncation and numbers being stored inaccurately - The range of the fixed point binary number is limited by the fractional part requiring a lot of bits to store. This means storing fixed point binary numbers is extremely resource intensive