Number Systems And Binary

Question 1

What are the two binary digits

Answer 1

1 & 0

Question 2

Represent 134 in Binary

Answer 2

10000110

Question 3

What is the largest binary number held in 8 bits?

Answer 3

255

Question 4

What does MSB stand for?

Answer 4

Most Significant Bit

Question 5

What does LSB stand for?

Answer 5

Least Significant Bit

Question 6

Represent 136.75 in Binary form

Answer 6

10001000.1100

Question 7

How are negative numbers stored?

Answer 7

Using two’s compliment

Question 8

Explain how to convert negative numbers to binary

Answer 8

1) Convert positive number to binary
2) Starting from right hand side copy all bits up-to and including first 1
3)Flip all other bits

Question 9

How to do binary subtraction with negative numbers

Answer 9

1)Convert negative number to binary
2) Using two’s compliment represent the negative number in binary
3) Add to the positive number

Question 10

Perform Binary subtraction on 8-6

Answer 10

100000010
(Overflow occurs so 1 at beginning doesn’t count)

Question 11

List the rules for addition in binary

Answer 11

0+0=0
0+1=1
1+0=1
1+1=0 carry the one
1+1+1=1 carry the one

Question 12

Using binary addition add 00011+0001

Answer 12

00100

Question 13

Name the steps for binary multiplication:

Answer 13

1)Copy Both numbers to binary and approach like long multiplication
2) Copy top bit line whenever you see a 1 in bottom bit line.
3) Whenever you have to copy out a line again shift one to left.
4) Then add together

Question 14

Multiply 8 by 3 using binary multiplication.

Answer 14

8x3=11000

Question 15

Explain the repeated division by two method

Answer 15

An easy method of converting decimal to binary by writing down decimal number and continuously dividing by 2 to give a result and remainder of either 1 or 0. Until the final result is equal to 0. MSB from bottom and LSB on top.

Question 16

Convert the number 89 to binary using divide by 2 method

Answer 16

1011001

Question 17

What base system is Hexadecimal?

Answer 17

16

Question 18

What are benefits of hex?

Answer 18

-Simplifies big numbers
-Easier to remember and understand
-More compact when displayed
-Less likely of an error when typing data

Question 19

Convert 10010010 to hex

Answer 19

92

Question 20

Convert Hex 3CF to binary

Answer 20

001111001111

Question 21

Natural Numbers

Answer 21

All positive whole numbers including 0

Question 22

Integer Numbers

Answer 22

All whole numbers both positive and negative

Question 23

Rational Numbers

Answer 23

Set of numbers that can be written as fractions

Question 24

Irrational

Answer 24

A number that can’t be written as a fraction eg surds

Question 25

Real Numbers

Answer 25

Set of all possible real world quantities (any number)

Question 26

Ordinal Numbers

Answer 26

Used to tell objects position

Question 27

What is kibi as a value?

Answer 27

2^10 or 1024

Question 28

What is Mebi as a value?

Answer 28

2^20 or 1048576

Question 29

What is Gibi as a value?

Answer 29

2^30 or 1073741824

Question 30

What is the value of Tebi?

Answer 30

2^40 or 1099511627776

Question 31

What is the value of kilo, mega,giga and tera

Answer 31

10^3,10^6,10^9,10^12

Question 32

What is a floating point number?

Answer 32

Numbers that contain floating decimal point

Question 33

How do floating point numbers work?

Answer 33

Using a : Significant-contains numbers digits Exponent-says whether decimal point is placed relative to beginning of significand.

Question 34

What are benefits of floating point numbers?

Answer 34

-It can represent numbers at wildly different magnitudes -Provides same relative accuracy at all magnitudes -Allows calculations across magnitudes

Question 36

Using mantissa and exponent convert 23.25 using 8 bit mantissa and 5 bit exponent.

Answer 36

0.1011101 00101

Question 37

Convert -7.25 using 8 bit mantissa and 5 bit exponent

Answer 37

1.000110 00011

Question 38

What are limitations of floating point numbers?

Answer 38

Overflow- A number that is too large to store in available number of bits or storage space. Underflow- A result that is so close to 0.

Question 39

How do you calculate Absolute error?

Answer 39

Absolute error=Expected value-Value you got

Question 40

What is relative error?

Answer 40

Relative error= Absolute error/Actual Value