4.5 Data Representation

Question 1

What do you use to represent negative numbers in binary?

Answer 1

2’s complement

Question 2

What is it called when you have a leftover carry bit after addition in binary?

Answer 2

An overflow

Question 3

What is the quickest way to multiply a binary number by 2?

Answer 3

Shift each column to the left by one padding the right with zeros

Question 4

What is the quickest way to multiply a binary number by 4?

Answer 4

Shift each column to the left by two padding the right with zeros

Question 5

When using 2’s complement what is the MSB used as?

Answer 5

A sign bit

Question 6

What is the main method we use to convert a number into a negitave using twos compliment?

Answer 6

Starting from the LSB copy up to and including the first one after that continue down the number and invert each bit

Question 7

What does LSB stand for?

Answer 7

Least significant bit

Question 8

What does MSB stand for?

Answer 8

Most significant bit

Question 9

What is the method we dont use to convert a number into a negitave using twos compliment?

Answer 9

Invert all bits then add one

Question 10

How do we subtract one number from another in binary?

Answer 10

Convert the number you wish to subtract into 2’s compliment and then add them

Question 11

When there is overflow when subtracting what do you do about it?

Answer 11

Nothing, you ignore it

Question 12

What are the types of numbers?

Answer 12

Rational, Irrational, Natural, Integer, Real and Ordinal

Question 13

What letter symbols represent irrational numbers?

Answer 13

Q and R

Question 14

What letter symbols represents natural numbers?

Answer 14

N

Question 15

What letter symbols represents integers?

Answer 15

Z

Question 16

What is the basic definition for rational numbers?

Answer 16

It is a number that can be represented by two integers in a fraction.

Question 17

What is the basic definition for irational numbers?

Answer 17

It is a number that cannot be represented by two integers in a fraction.

Question 18

What is the basic definition for real numbers?

Answer 18

It is a number that is not imaginary

Question 19

What is the basic definition for intigers?

Answer 19

It is a number that has no decimal places (Whole numbers)

Question 20

What is the basic definition for ordinal numbers?

Answer 20

It is a number that is used for indexing and is thus a position on a list

Question 21

What is the basic definition for natural numbers?

Answer 21

It is a number that is greater than or equal to 0 and is whole (not negative)

Question 22

Describe a set of rational numbers

Answer 22

A set of rational numbers would be numbers where the numerator and denominators are whole numbers

Question 23

Why are all integers rational numbers?

Answer 23

Because all integers can be written as a fraction as they are all divisible by one

Question 24

How do you what do you use to represent fractions in binary?

Answer 24

You use fixed point notation

Question 25

What are the first four colum headings in after the fixed point in both power and index form?

Answer 25

2^-1, 2^-2, 2^-3, 2^-4 | 1/2, 1/4, 1/8, 1/16

Question 26

What does adding a fixed point to a binary number do to the range if you keep the same number of bits?

Answer 26

It reduces the range as the MSB will have a lower heading

Question 27

What does adding a fixed point to a binary number do to the accuracy if you keep the same number of bits?

Answer 27

It increases the acuracy as you can make it more precise.

Question 28

Can all fractions be represented with fixed point bits?

Answer 28

No, you just have to get as close to the original number as you can

Question 29

What is the formula to calculate the largest postive number possible when using 2's compliment where n is the number of bits?

Answer 29

2^(n-1)-1

Question 30

What is the formula to calculate the largest negative number possible when using 2's compliment where n is the number of bits?

Answer 30

2^(n-1)

Question 31

How do you calculate the highest possible number in a normal binary number where n is the number of bits?

Answer 31

2^n - 1

Question 32

How do you calculate the range of a normal binary number where n is the number of bits?

Answer 32

2^n