Unit 6 - Data Types

Question 1

binary addition rules

Answer 1

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 1 = 0 carry 1
• 1 + 1 + 1 = 1 carry 1

Question 2

what is an overflow

Answer 2

when the arithmetic result exceeds the available number of bits

Question 3

what does one shift to the left do

Answer 3

x 2

Question 4

what does one shift to the right do

Answer 4

/2

Question 5

how does twos complement work

Answer 5

-128, 64, 32, 16, 8, 4, 2, 1

Question 6

how to work out if the denary value will be positive or negative in twos complement

Answer 6

starts with 0 = positive
starts with 1 = negative

Question 7

how convert a negative denary number to binary

Answer 7

• flip all of the bits
• add 1

Question 8

how to convert a negative twos complement binary number to denary

Answer 8

• flip the bits
• add one
• negative sign in-front of byte
• convert

Question 9

how to do binary subtraction using twos complement

Answer 9

• convert negative binary number into twos complement
• add positive binary value and twos complement value

Question 10

why are fixed point binary number useful

Answer 10

• represent fractions in binary
• increased performance

Question 11

what is limited by fixed point binary

Answer 11

• range

Question 12

advantages of floating point binary

Answer 12

• greater range
• greater accuracy

Question 13

what does moving the point to the right in floating point binary do

Answer 13

increase range
reduces precision

Question 14

what does moving the point to the left in floating point binary do

Answer 14

reduces range
increases precision

Question 15

what is the mantissa

Answer 15

the coefficient

Question 16

what is the exponent

Answer 16

the order of magnitude

Question 17

positive exponent means

Answer 17

decimal point moves right

Question 18

negative exponent means

Answer 18

decimal point moves left

Question 19

how to handle negative exponents

Answer 19

• twos complement of exponent
• move the binary point of the mantissa by exponent to the left
• translate to denary

Question 20

how to handle negative mantissas

Answer 20

• find twos complement of mantissa
• translate exponent to denary
• move binary point by exponent to the right
• translate this to binary

Question 21

what does the sign bit show

Answer 21

positive or negative value of mantissa
- 0. = positive
- 1. = negative

Question 22

what is normalisation

Answer 22

process of moving the binary point of a floating point number to provide the maximum level of precision for a given number of bits. this is achieved by ensuring that the first digit after the binary pin t is a significant digit

Question 23

how to normalise a positive binary number

Answer 23

a positive number has a sign but if 0 and the next digit is always 1. this means the mantissa of a positive number in normalised for always lies between 1/2 and 1

Question 24

normalising a negative binary number

Answer 24

a normalised negative number has a sign but of 1 and the next bit is always 0

Question 25

increase size of mantissa

Answer 25

greater precision

Question 26

increase size of exponent

Answer 26

increase range

Question 27

how convert from denary to normalised binary floating point

Answer 27

- convert to fixed point binary - then use an exponent to make the mantissa normalised

Question 28

how to do floating point addition and subtraction

Answer 28

- line up the points by making the exponents equal - add or subtract the mantissas - normalise the result

Question 29

what is an under flow error

Answer 29

when a result is to small to be represented by the allotted number of bits

Question 30

what is a logical shift

Answer 30

all the bits move right or left. a logical shift causes the least significant bit to be shifted into the carry bit and a zero moves into the most significant bit to occupy the vacated space

Question 31

what is an arithmetic shift

Answer 31

similar to a logical shift but takes into account the sign bit, which always remains the same. therefore the first or last bit of the mantissa moves into the carry bit and the sign bit remains the same

Question 32

how to multiply two binary numbers

Answer 32

- use addition and shifts

Question 33

what is a circular shift

Answer 33

a rotate or circular shift is useful for performing shifts in multiple bytes. in a circular shift right, the value in the least significant bit is moved into the carry bit, and the carry bit is moved into her most significant bit

Question 34

what does an AND mask do

Answer 34

extracts - to clear a particular bit, use a mask of 0 and the AND operator - use a mask of 1 to leave a bit unchanged

Question 35

what does an OR mask do

Answer 35

sets - to set a particular bit, use a mask of 1 and the OR operator. - use a mask of 0 to leave a bit unchanged

Question 36

what does an XOR mask do

Answer 36

toggles - to toggle a particular bit, use a mask of 1 and the XOR operator - use a mask of 0 to leave a bit unchanged

Question 37

order of binary prefixes

Answer 37

- kibi- KiB - 2^10 - mebi - MiB - 2^20 - gibi- GiB - 2^30 - tebi- TiB - 2^40

Question 38

what is a primitive data type

Answer 38

one which is provided by a programming language

Question 39

what is a composite data type

Answer 39

not considered a primitive data type for example an array

Question 40

name the number bases and their base

Answer 40

denary - base 10 binary - base 2 hexadecimal - base 16

Question 41

name the character sets

Answer 41

- 7-bit ASCII - 8-bit ASCII - Unicode

Question 42

how do character sets represent text

Answer 42

each character, number and symbol has a uniquely defined code