Number systems

What is digital systems

What is the formula to find the number of bits the message needs

Round it up

Is Shannon’s theorem specific to binary numbers?

What is a number system

What is information?

What is a decimal number?

What is the algorithm for converting decimal to binary (sum of weights)

What is the algorithm for converting decimal to binary (Repeated division by 2)

How to set up the table for sum of weights

How to set up the table for repeated division by 2

How to convert binary to hexadecimal

How to convert hexadecimal to binary

How to convert hexadecimal to decimal

How to convert decimal to hexadecimal?

This idea applies to any base

How to convert binary fractions to decimal fractions?

How to convert hexadecimal fractions to decimal fractions

This idea applies to all bases

How is a sign/magnitude binary number represented?

How to do one’s complement

What is the issue with sign/magnitude and one’s complement

Both of them have 2 representation for 0 (therefore makes arithmetic complex)

How to do two’s complement

Same method to go positive number

How to convert decimal to binary fraction

Same idea applies for all bases

What are special names for different storing sizes

What is an easy way to figure out of there is an overflow

How to multiply in binary

Same idea when for decimal. Only difference is (1×1 = 1 while other is just 0)

How is the floating point stored using IEEE 752 floating point representation?

This is how computer stores floats

For IEEE 754 floating point, why is there a bias?

To avoid 2’s complement

What are the steps for IEEE 754?

1. Determine the sign bit

2. Convert decimal to binary

3. Normalise to scientific notation (1.something x 2^exponent)

4. Apply the bias to the exponent (+127)

5. Extract the mantissa (23 bits & after the implied leading 1)