1.4.1 - Data Types - Using binary

Question 1

Primitive data types

Answer 1

One provided by a programming language

Integer, float, char, string, Boolean

Question 2

Denary

Answer 2

Base 10/decimal

Our number system

Question 3

How to know what data type a value is in

Answer 3

It will have 2/10/16 written in subscript

Question 4

Binary

Answer 4

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

The bases are all powers of 2

Question 5

Converting from denary to binary

Answer 5

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

Question 6

Hexadecimal

Answer 6

Uses base 16

Letters A-F represent values 10-15

Question 7

Hexadecimal advantages

Answer 7

Quicker
Easier to understand
Less likely to make errors

Question 8

Converting hex to denary

Answer 8

Show workings

Convert letters to digits, multiply by base and sum

Question 9

Converting denary to hex

Answer 9

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

Question 10

Hex and binary conversions

Answer 10

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

Question 11

Binary addition

Answer 11

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

Question 12

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

Answer 12

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

Question 13

Range of Binary Addition

Answer 13

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

Question 14

Binary Subtraction

Answer 14

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

Question 15

Sign and Magnitude

Answer 15

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

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

Question 16

Two’s Complement Grid

Answer 16

The leftmost column has the negative value of itself

Question 17

Sign and Magnitude Range

Answer 17

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

Question 18

Two’s Complement Process

Answer 18

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

Question 19

Two’s complement range

Answer 19

• (2^(n-1)) -> 2^(n-1) - 1

Question 20

What happens if there is overflow in binary subtraction?

Answer 20

You can ignore those bits

Question 21

What are the lsb and msb

Answer 21

lsb - least significant bit - the rightmost bit

msb - most significant bit - the leftmost bit

Question 22

Logical shift left

Answer 22

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

Question 23

Logical shift right

Answer 23

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

Question 24

Logical shift sums

Answer 24

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

Question 25

Arithmetic shift left

Answer 25

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

Question 26

Arithmetic shift right

Answer 26

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

Question 27

Arithmetic shift sums

Answer 27

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

Question 28

Circular shift left

Answer 28

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

Question 29

Circular shift right

Answer 29

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

Question 30

Bitwise Masks

Answer 30

Apply another binary value with an AND, OR or XOR | Use boolean algebra on binary values by using each pair of corresponding values

Question 31

OR masking

Answer 31

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

Question 32

AND masking

Answer 32

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

Question 33

XOR masking

Answer 33

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

Question 34

Fixed point binary

Answer 34

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

Question 35

First 5 coefficients after the fixed point

Answer 35

0.5, 0.25, 0.125, 0.0625, 0.03125

Question 36

How does moving the decimal point affect it?

Answer 36

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

Question 37

What is a floating point binary number made up of

Answer 37

A mantissa and an exponent | mantissa x 2^exponent

Question 38

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

Answer 38

Between the first 2 bits

Question 39

Positive floating point -> decimal

Answer 39

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

Question 40

Negative floating point -> decimal

Answer 40

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

Question 41

How to know if a mantissa/exponent is negative

Answer 41

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

Question 42

Negative Exponents decimal conversions

Answer 42

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

Question 43

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

Answer 43

Add the 1 to the lsb

Question 44

Normalised positive number

Answer 44

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

Question 45

Normalising a positive number

Answer 45

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

Question 46

Normalised negative number

Answer 46

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

Question 47

Normalising a negative number

Answer 47

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

Question 48

Positive denary -> floating point binary

Answer 48

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

Question 49

Negative denary-> floating point binary

Answer 49

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

Question 50

Floating point addition

Answer 50

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

Question 51

Floating point subtraction

Answer 51

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