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Comp Science > 4.5 Data Representation > Flashcards

4.5 Data Representation Flashcards

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1
Q

What do you use to represent negative numbers in binary?

A

2’s complement

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2
Q

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

A

An overflow

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3
Q

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

A

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

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4
Q

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

A

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

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5
Q

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

A

A sign bit

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6
Q

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

A

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

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7
Q

What does LSB stand for?

A

Least significant bit

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8
Q

What does MSB stand for?

A

Most significant bit

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9
Q

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

A

Invert all bits then add one

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10
Q

How do we subtract one number from another in binary?

A

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

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11
Q

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

A

Nothing, you ignore it

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12
Q

What are the types of numbers?

A

Rational, Irrational, Natural, Integer, Real and Ordinal

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13
Q

What letter symbols represent irrational numbers?

A

Q and R

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14
Q

What letter symbols represents natural numbers?

A

N

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15
Q

What letter symbols represents integers?

A

Z

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16
Q

What is the basic definition for rational numbers?

A

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

17
Q

What is the basic definition for irational numbers?

A

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

18
Q

What is the basic definition for real numbers?

A

It is a number that is not imaginary

19
Q

What is the basic definition for intigers?

A

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

20
Q

What is the basic definition for ordinal numbers?

A

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

21
Q

What is the basic definition for natural numbers?

A

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

22
Q

Describe a set of rational numbers

A

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

23
Q

Why are all integers rational numbers?

A

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

24
Q

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

A

You use fixed point notation

25
Q

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

A

2^-1, 2^-2, 2^-3, 2^-4

1/2, 1/4, 1/8, 1/16

26
Q

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

A

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

27
Q

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

A

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

28
Q

Can all fractions be represented with fixed point bits?

A

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

29
Q

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

A

2^(n-1)-1

30
Q

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

A

2^(n-1)

31
Q

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

A

2^n - 1

32
Q

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

A

2^n

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