1-2: Number Systems And Binary

Question 1

explain how binary works

Answer 1

as we move from right to left, each digit is worth twice as much as the previous one.
2^0, 2^1, 2^2, 2^3, 2^4……

Question 2

what is the range of values that an 8 bit integer can store

Answer 2

256
(0-255)

Question 3

what is the largest binary number that can be held in 8 bits

Answer 3

255

Question 4

what is one byte

Answer 4

8 bits

Question 5

what do computers always begin their count from

Answer 5

0

Question 6

explain the method of twos complement

Answer 6

-convert the positive integer into binary
-starting from the right-hand side copy all bits up to and including the one
-flip all other bits

Question 7

what are the 5 basic binary addition rules

Answer 7

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 (carry the one)
1 + 1 +1(has been carried over) = 1 (carry the one)

Question 8

how do you subtract binary numbers

Answer 8

-convert the negative number to binary
-using twos complement represent the negative number
-convert the other number to binary
-add the numbers together

Question 9

how do you multiply numbers in binary

Answer 9

Step 1: Write down the multiplicand
and the multiplier(one below the other in proper positions).

Step 2: Multiply the rightmost digit or the least significant bit (LSB) of the multiplier with all the digits of the multiplicand

Step 3: Add a placeholder of ‘0’ before multiplying the next higher-order digit of the multiplier& with the multiplicand.

Step 4: Repeat the same process for all the next higher-order digits until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand with the multiplier.

Step 5: The product obtained in each row is called the partial product. Finally, add all the partial products. To add all the binary numbers use the rules of binary addition.

Question 10

what is base 2, base 10 and base 16

Answer 10

base 2 is binary
base 10 is denary
base 16 is hex

Question 11

explain what the numbers in hex are

Answer 11

0 - 9 = 0 to 9
10 - 15 = A to F

Question 12

what are natural numbers and give an example

Answer 12

positive whole numbers
Eg, 1

Question 13

what are integer numbers and give an example

Answer 13

positive and negative whole numbers
Eg, -3 and 5

Question 14

what are rational numbers and give an example

Answer 14

set of numbers that can be written as fractions. Since a number such as 7 can be written as 7/1 all integers are rational numbers

Question 15

what are irrational numbers and give an example

Answer 15

one that cannot be written as a fraction
Eg, square root of 2 or pi

Question 16

what are real numbers and give an example

Answer 16

set of possible real world quantaties
Eg, every number basically

Question 17

what are ordinal numbers and give an example

Answer 17

when objects are placed in order
Eg, in lists or arrays

Question 18

what is the symbol for natural numbers

Answer 18

N

Question 19

what is the symbol for integer numbers

Answer 19

Z

Question 20

what is the symbol for rational numbers

Answer 20

Q

Question 21

what is the symbol for real numbers

Answer 21

R

Question 22

give the power of kibi and the value

Answer 22

2^10
1024

Question 23

give the power of mebi and the value

Answer 23

2^20
1048576

Question 24

give the power of gibi and the value

Answer 24

2^30
1073741824

Question 25

give the power of tebi and the value

Answer 25

2^40
1099511627776

Question 26

give the power of kilo and the value

Answer 26

10^3
1000

Question 27

give the power of mega and the value

Answer 27

10^6
1000000

Question 28

give the power of giga and the value

Answer 28

10^9
1000000000

Question 29

give the power of tera and the value

Answer 29

10^12
1000000000000