Data Types Flashcards
What are the 5 primitive data types?
- integer
- real/floating point
- character
- string
- boolean
What is an integer?
- a whole number with no fractional/decimal parts
- Can be positive or negative
- useful for counting things
What is a real/floating point number?
- positive or negative number which can but don’t need a fractional part
- useful for measuring things
- all integers are real numbers
What is a character?
- a single symbol used by a computer
- Eg. The letters of the alphabet, numbers, special characters
What is a string?
- 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)
What is a Boolean?
- 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
What is the human counting system?
Base 10 - denary
What is the computer counting system?
Base 2 - binary
A single binary digit is a …
Bit
8 binary digits combined is a …
Byte
4 binary digits combined is a …
Nybble
How do you convert from binary to denary?
- 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
How do you convert from denary to binary?
- 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
What are the binary addition rules?
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)
What are the binary addition rules?
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)
How would you represent a binary number as a whole number of bytes?
You would add leading 0’s (0’s in front of the actual number) - these don’t affect the value of the binary number
How do you do binary addition?
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
what are the basic binary subtraction rules?
0-0=1
1-0=1
1-1=0
0-1=1 (borrow 1 from the adjacent higher order digit)
how do you do basic binary subtraction?
do it like normal column subtraction following the rules of binary subtraction and doing carries where you need to
what sort of counting system is hexadecimal?
base 16
how do you represent values 10-15 using hexadecimal?
using letters A-F
A=10, B=11, C=12, D=13, E=14, F=15
How do you convert from hexadecimal into denary?
- 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
how do you convert from denary to hex?
- divide the number by 16
- the remainder will be the rightmost hex value
- if there’s no remainder then rightmost digit will be 0
how do you convert from hex to binary?
- 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
how do you convert from binary to hex?
- divide the binary number into nybbles
- convert the nybble into a denary digit
- convert this into hex digits and recombine the hex digits together
how do you represent a negative binary number using sign magnitude?
- 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
why is sign magnitude not the best way of representing negative numbers?
you can’t do any mathematical operations on the numbers when they’re in this format - the maths goes funny
How do you represent negative binary numbers in two’s compliment?
- 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
how do you convert out of two’s complement to find the denary number?
- 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
how do you do binary subtraction using two’s complement?
- binary subtraction is basically the same as adding a negative
- so just add the negative number(s) together using binary column addition
what is floating point binary?
- 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
how do you understand floating point binary (mantissa + exponent)?
- 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
what is normalisation?
- 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
how do you normalise a number?
- 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
how do you add floating point binary numbers?
- 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
how do you subtract floating point binary numbers?
- make the exponents the same and manipulate the mantissa
- then do normal binary subtraction
- then normalise the result if needed
what is a shift?
- 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
What is a right shift?
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
what is a left shift?
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
what is the difference between shifting a signed bit and unsigned bit?
- 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
What are some potential issues of doing a shift?
- overflow error - data lost during left shift
- underflow error - data lost during right shift
What is masking?
use a binary number as a mask and combine it with a logic gate to give a different output
can be used for encryption
what is a NOT mask?
follows same logic as NOT logic gate:
- reverses the binary bits - 1 -> 0, 0 -> 1
what is an AND mask?
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
what is an OR mask?
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
what is an XOR mask?
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
