4.5: section 3: data representation: number, binary and information coding systems

Question 1

what are natural numbers and their set letter

Answer 1

all positive whole numbers including 0 used for counting

N={0,1,2,3}

Question 2

what are in integers and their set letter

Answer 2

any positive or negative whole number

Z={…-2,-1,0,1,2,3}

Question 3

what are rational number and their set letter

Answer 3

values expressed as fractions or ratios
Q={…2/1,2/2,2/3,2/4…}
Q={…2.1,0.6,0.5}]

Question 4

what are real numbers

Answer 4

numbers that are rational or irrational and are used for measurement

Question 5

what are ordinal numbers

Answer 5

not real or natural numbers and are used to show position

Question 6

what are irrational numbers

Answer 6

a number that cannot be written as a fraction

I = { pi }

Question 7

what type of numbers are used for counting

Answer 7

natural numbers

Question 8

what type of numbers are used for measurement

Answer 8

real numbers

Question 9

what are base 10 numbers

Answer 9

decimal numbers which are all represented with a selection of 10 digits
0,1,2,3,4,5,6,7,8,9

Question 10

what are base 2 numbers

Answer 10

binary numbers which are all represented with a selection of 2 digits
1,0

Question 11

what are base 16

Answer 11

hexadecimal numbers which are all represented using a selection of 16 characters
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

Question 12

why is hexadecimal used

Answer 12

hexadecimal is used as a shorthand for binary as it makes it easier to write and remember without making as many mistakes

Question 13

what is a bit

what is a byte

Answer 13

a bit is a single binary value

a byte is a set of 8 binary values

Question 14

what are the binary units

Answer 14

kilo, k - 10^3
kibi, Ki -2^10
mega, M - 10^6
mebi, Mi -2^20
giga, G - 10^9
gibi, Gi -2^30
tera, T - 10^12
tebi, Ti -2^40

Question 15

what is the difference between signed and unsigned binary

Answer 15

• unsigned binary can only be used to represent positive decimal numbers
• signed binary is used to represent both positive and negative binary numbers with coding schemes like twos complement

Question 16

what are some rules of binary addition

Answer 16

0+0=0
1+0=1
1+1 =10
1+1+1=11

Question 17

how is binary subtraction completed

Answer 17

one of the binary numbers is translated using twos compliment and then added to the other binary number

Question 18

how is binary multiplication completed

Answer 18

the binary number is shifted by the amount of spaces necessary

Question 19

what is an absolute error

Answer 19

the difference between the target number and the closest rounded number that can be represented

Question 20

what is a relative error

Answer 20

the absolute error divided by the target number as a percentage

Question 21

compare the range provided by fixed point and floating point binary

Answer 21

fixed: depends on the position of the binary point
the more digits to the left the greater the range but the lower the precision

floating: can easily represent large numbers and small fractions. more bits used for the exponent means increased range

Question 22

compare the precision provided by fixed point and floating point binary

Answer 22

fixed: depends on the position of the binary point
the more digits to the right the greater the precision but the lower the range

floating:more bits for the mantissa means increased precision

Question 23

compare the calculation speed needed for fixed point and floating point binary

Answer 23

fixed: simpler to calculate so the processing speed tends to be faster
floating: point has to be moved first which make sit longer to be processed and calculated

Question 24

why are binary numbers normalised

Answer 24

as there are multiple ways of representing a single integer in binary binary numbers are normalised so there is only one representation for each digit.

negative numbers start with 10

positive numbers start with 01