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A Level Computer Science Paper 1 > 1.4.1 - Data Types - Using binary > Flashcards

1.4.1 - Data Types - Using binary Flashcards

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1
Q

Primitive data types

A

One provided by a programming language

Integer, float, char, string, Boolean

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2
Q

Denary

A

Base 10/decimal

Our number system

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3
Q

How to know what data type a value is in

A

It will have 2/10/16 written in subscript

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4
Q

Binary

A

Uses 1/0 multiplied by the base, starting from the right

The bases are all powers of 2

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5
Q

Converting from denary to binary

A

Put a 1 in the column that is closest to the denary value, subtract and repeat

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6
Q

Hexadecimal

A

Uses base 16

Letters A-F represent values 10-15

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7
Q

Hexadecimal advantages

A

Quicker
Easier to understand
Less likely to make errors

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8
Q

Converting hex to denary

A

Show workings

Convert letters to digits, multiply by base and sum

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9
Q

Converting denary to hex

A

Divide by 16, add the hex symbol of the remainder assuming 2 bit value

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10
Q

Hex and binary conversions

A

Each hex value is 4 bits of binary
Convert the hex or binary to digit and then write out as the other
Combine the outputs

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11
Q

Binary addition

A

Works similar to denary, carry over a 1 if you have to go back to 0

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12
Q

What happens if adding 2 8-bit numbers gives a 9-bit answer?

A

There is an overflow error and the computer just cuts off the last bit from its output
Clearly indicate this in your answers

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13
Q

Range of Binary Addition

A

0 -> (2^n) -1 where n is the number of bits

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14
Q

Binary Subtraction

A

You make the second number into its negative value using Two’s Complement and then add them

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15
Q

Sign and Magnitude

A

The first bit represents +/- and then the rest are the same

The first bit being a 1 means the number is negative.

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16
Q

Two’s Complement Grid

A

The leftmost column has the negative value of itself

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17
Q

Sign and Magnitude Range

A

-(2^(n-1) + 1 -> (2^)n-1)) -1

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18
Q

Two’s Complement Process

A
  1. Find the positive value
  2. Invert the value of each bit
  3. Add one
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19
Q

Two’s complement range

A
  • (2^(n-1)) -> 2^(n-1) - 1
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20
Q

What happens if there is overflow in binary subtraction?

A

You can ignore those bits

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21
Q

What are the lsb and msb

A

lsb - least significant bit - the rightmost bit

msb - most significant bit - the leftmost bit

22
Q

Logical shift left

A

Pushes every value 1 space to the left, the msb goes into the carry bit, 0 comes into the lsb

23
Q

Logical shift right

A

Pushes every value 1 space to the right, the lsb goes into the carry bit, 0 comes into the msb

24
Q

Logical shift sums

A

x2 for left, /2 for right as long as it isn’t two’s complement or sign and magnitude

25
Q

Arithmetic shift left

A

Pushes every value 1 space to the left but the msb doesn’t move so the second bit from the left goes into the carry bit, 0 comes in as lsb

26
Q

Arithmetic shift right

A

Pushes every value 1 space to the right and the value that comes into the msb is whatever was there before

27
Q

Arithmetic shift sums

A

x2 for left, /2 for right, for all numbers

28
Q

Circular shift left

A

Pushes every value 1 space to the left, the msb into the carry bit and the carry bit into the lsb

29
Q

Circular shift right

A

Pushes every value 1 space to the right, the lsb into the carry bit and the carry bit into the msb

30
Q

Bitwise Masks

A

Apply another binary value with an AND, OR or XOR

Use boolean algebra on binary values by using each pair of corresponding values

31
Q

OR masking

A

0: The output is the same as the input
1: The output is 1 (set the bit)

32
Q

AND masking

A

0: The output is 0 (clear the bit)
1: The output is the same as the input

33
Q

XOR masking

A

0: The output is the same as the input
1: The output is the opposite of the input (toggle the bit)

34
Q

Fixed point binary

A

At a fixed point is a metaphorical decimal point, after that comes negative values of 2

35
Q

First 5 coefficients after the fixed point

A

0.5, 0.25, 0.125, 0.0625, 0.03125

36
Q

How does moving the decimal point affect it?

A

Having more bits before the decimal point increases the range but decreases the accuracy

37
Q

What is a floating point binary number made up of

A

A mantissa and an exponent

mantissa x 2^exponent

38
Q

Where is the decimal point at the start in floating point binary?

A

Between the first 2 bits

39
Q

Positive floating point -> decimal

A
  1. Find the value of the exponent
  2. Move the decimal point by that many spaces to the right
  3. Find the value of that as if it was a fixed point decimal
40
Q

Negative floating point -> decimal

A
  1. Find the two’s complement of the mantissa
  2. Find the value of the exponent
  3. Move the decimal point that many spaces to the right
  4. Find the value as if it was a fixed point decimal
  5. Put a sign in front of your value
41
Q

How to know if a mantissa/exponent is negative

A

It will have a 1 as the msb (in two’s complement)

42
Q

Negative Exponents decimal conversions

A
  1. Find the value of the exponent remembering the negative left value
  2. Move the decimal point that many places to the left, as if there were all 0s to the left of your number
  3. Find the value as if it was a regular fixed point number
43
Q

Doing two’s complement on a binary number with a point

A

Add the 1 to the lsb

44
Q

Normalised positive number

A

Has a sign bit 0 and a 1 for the next bit

45
Q

Normalising a positive number

A
  1. Move the decimal point to the right until it is in front of the 1
  2. Add as many zeroes to the end as you moved right by
  3. Subtract the amount of spaces you moved to the right from the exponent
  4. Write out the normalised number with the mantissa and exponent
46
Q

Normalised negative number

A

Has a sign bit 1 and a 0 for the next bit. Leading 1s don’t change the value.

47
Q

Normalising a negative number

A
  1. Move the decimal point to the right until it is in front of a 0
  2. Add as many zeroes to the end as you moved right by
  3. Subtract the amount of spaces you moved to the right from the exponent
  4. Write out the normalised number with the mantissa and exponent
48
Q

Positive denary -> floating point binary

A
  1. Convert it to fixed point binary
  2. Move the decimal point to the left until it is in front of the first 1
  3. Pad the RHS with zeroes to keep the same length if necessary
  4. Set the exponent equal to how many spaces you moved to the left
49
Q

Negative denary-> floating point binary

A
  1. Convert the positive number to fixed point (write a 0 at the start)
  2. Take the two’s complement
  3. Convert as you would a positive number
50
Q

Floating point addition

A
  1. Convert each floating point number to fixed point binary by shifting the binary point right by the value of the exponent
  2. Sum the two values
  3. Convert back to floating point and normalise
51
Q

Floating point subtraction

A
  1. Convert each floating point number to fixed point binary by shifting the binary point right by the value of the exponent
  2. Take the two’s complement of the negative value
  3. Sum the two values
  4. Convert back to floating point and normalise

A Level Computer Science Paper 1 (23 decks)

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