Data Types

Question 1

What are the 5 primitive data types?

Answer 1

• integer
• real/floating point
• character
• string
• boolean

Question 2

What is an integer?

Answer 2

• a whole number with no fractional/decimal parts
• Can be positive or negative
• useful for counting things

Question 3

What is a real/floating point number?

Answer 3

• positive or negative number which can but don’t need a fractional part
• useful for measuring things
• all integers are real numbers

Question 4

What is a character?

Answer 4

• a single symbol used by a computer
• Eg. The letters of the alphabet, numbers, special characters

Question 5

What is a string?

Answer 5

• a collection of characters
• can store a single character or many characters in succession
• useful for storing text and phone numbers starting in 0 (normal integers or floating point would get rid of the starting 0)

Question 6

What is a Boolean?

Answer 6

• values of this data type are restricted to True and False
• useful for storing data that can only take 2 values eg. the state of a power button

Question 7

What is the human counting system?

Answer 7

Base 10 - denary

Question 8

What is the computer counting system?

Answer 8

Base 2 - binary

Question 9

A single binary digit is a …

Answer 9

Bit

Question 10

8 binary digits combined is a …

Answer 10

Byte

Question 11

4 binary digits combined is a …

Answer 11

Nybble

Question 12

How do you convert from binary to denary?

Answer 12

• the least significant bit is the one furthest right
• The most significant bit is the one furthest left
• the value of the columns increase by a power of 2 each one you move further right
• if the column has a 1 in it counts the value of that column once, if there is a 0 don’t count it
• add the value of all the columns with a 1 in them to get the binary number in denary

Question 13

How do you convert from denary to binary?

Answer 13

• find the largest power of 2 which is smaller than the number you are converting, the write out the binary place values up to this value
• subtract this value from the original value, then repeat the process until you have 0.
• Make sure all the binary bits with 1s add up to the original value

Question 14

What are the binary addition rules?

Answer 14

0+0+0=1
0+0+1=1
0+1+1=10 (1 is carried to next column in column addition)
1+1+1=11 (1 is carried over to next column in column addition)

Question 15

What are the binary addition rules?

Answer 15

0+0+0=1
0+0+1=1
0+1+1=10 (1 is carried to next column in column addition)
1+1+1=11 (1 is carried over to next column in column addition)

Question 16

How would you represent a binary number as a whole number of bytes?

Answer 16

You would add leading 0’s (0’s in front of the actual number) - these don’t affect the value of the binary number

Question 17

How do you do binary addition?

Answer 17

Do it like column addition - like up the 2 binary numbers in columns using 1s column to like them up and then apply binary addition rules
If there is a carry then put the carried one in small under the next column to the left

Question 18

what are the basic binary subtraction rules?

Answer 18

0-0=1
1-0=1
1-1=0
0-1=1 (borrow 1 from the adjacent higher order digit)

Question 19

how do you do basic binary subtraction?

Answer 19

do it like normal column subtraction following the rules of binary subtraction and doing carries where you need to

Question 20

what sort of counting system is hexadecimal?

Answer 20

base 16

Question 21

how do you represent values 10-15 using hexadecimal?

Answer 21

using letters A-F
A=10, B=11, C=12, D=13, E=14, F=15

Question 22

How do you convert from hexadecimal into denary?

Answer 22

• use the place values of hex and multiply by the column place value
• each column has a place value to the power of 16, with powers increasing the further left you move along

Question 23

how do you convert from denary to hex?

Answer 23

• divide the number by 16
• the remainder will be the rightmost hex value
• if there’s no remainder then rightmost digit will be 0

Question 24

how do you convert from hex to binary?

Answer 24

• convert each hex digit to a denary digit and then convert this into a binary nybble (4 bits)
• then recombine all the nybbles in the right order to get the binary number

Question 25

how do you convert from binary to hex?

Answer 25

- divide the binary number into nybbles - convert the nybble into a denary digit - convert this into hex digits and recombine the hex digits together

Question 26

how do you represent a negative binary number using sign magnitude?

Answer 26

- Use the first bit - the most significant figure - as the sign bit - the rest of the number is the magnitude - the actual number - a leading 1 means a negative number - a leading 0 means a positive number

Question 27

why is sign magnitude not the best way of representing negative numbers?

Answer 27

you can't do any mathematical operations on the numbers when they're in this format - the maths goes funny

Question 28

How do you represent negative binary numbers in two's compliment?

Answer 28

- also works by making the most significant bit negative but it does this mathematically rather than simply saying it is negative - convert the number into binary but the positive version - change all 0's into 1's, all 1's into 0's - add 1 to the flipped version

Question 29

how do you convert out of two's complement to find the denary number?

Answer 29

- subtract 1 from the two's complement number - flip the result 1's -> 0's, 0's -> 1's - convert this into denary - remember to make the denary number negative

Question 30

how do you do binary subtraction using two's complement?

Answer 30

- binary subtraction is basically the same as adding a negative - so just add the negative number(s) together using binary column addition

Question 31

what is floating point binary?

Answer 31

- kind of like standard form - split into mantissa and exponent - this is the info needed to work out what the actual value being represented is

Question 32

how do you understand floating point binary (mantissa + exponent)?

Answer 32

- convert it to positive binary if not already done - look at the mantissa first - take it to have a binary point after the first bit - convert the exponent to decimal - positive exponent = move the decimal point right - negative exponent = move the decimal point left

Question 33

what is normalisation?

Answer 33

- it is making sure that the mantissa of the floating point number is used as much as possible to make the value as precise as possible - essentially adjust it so that the mantissa starts in 01 (positive) or 10 (negative) - remove leading 0's/1's

Question 34

how do you normalise a number?

Answer 34

- split the number into a mantissa and exponent - adjust mantissa so that it starts in 01 or 10 - add zeroes to the start/end of mantissa if needed - if you make the mantissa bigger (move it along left) then reduce the exponent - if you make the mantissa smaller (move it along right) then increase the exponent

Question 35

how do you add floating point binary numbers?

Answer 35

- the exponents need to be equal - so equate it to the smaller exponent - change the mantissa to match the exponent - then do normal binary addition - normalise the result if needed

Question 36

how do you subtract floating point binary numbers?

Answer 36

- make the exponents the same and manipulate the mantissa - then do normal binary subtraction - then normalise the result if needed

Question 37

what is a shift?

Answer 37

- any shift done on a binary value is a logical shift - done by ALU - useful for division and multiplication - essentially shift all bit left or right a specified value - add leading/trailing 0's

Question 38

What is a right shift?

Answer 38

when the binary value is shifted to the right the specified number of places - it decreases the value of the binary number by the relevant power of 2

Question 39

what is a left shift?

Answer 39

when the binary value is shifted to the left the specified number of times - it increases the value of the the binary number by the relevant power of 2

Question 40

what is the difference between shifting a signed bit and unsigned bit?

Answer 40

- signed bit - pin the sign bit to the front of the number, then shift the rest of the number - unsigned bit - just shift all digits of the number

Question 41

What are some potential issues of doing a shift?

Answer 41

- overflow error - data lost during left shift - underflow error - data lost during right shift

Question 42

What is masking?

Answer 42

use a binary number as a mask and combine it with a logic gate to give a different output can be used for encryption

Question 43

what is a NOT mask?

Answer 43

follows same logic as NOT logic gate: - reverses the binary bits - 1 -> 0, 0 -> 1

Question 44

what is an AND mask?

Answer 44

follows the same logic as AND logic gate - 2 inputs gives the following outputs: 0+0=0 1+0=0 0+1=0 1+1=1

Question 45

what is an OR mask?

Answer 45

follows the same logic as OR gate - 2 inputs give the following outputs: 0+0=0 1+0=1 0+1=1 1+1=1

Question 46

what is an XOR mask?

Answer 46

follows the same logic as XOR gate - 2 inputs give the following outputs: 0+0=0 1+0=1 0+1=1 1+1=0