1&2 Number Systems And Binary

Question 1

How do you calculate the greatest number that can be created with x bits

Answer 1

(2^x)-1

Question 2

Which bit is the least significant bit

Answer 2

The right most bit

Question 3

Which bit is referred to as the most significant bit?

Answer 3

The left most bit

Question 4

How are decimals stored in binary?

Answer 4

They are stored as powers of 2^-x e.g. the mixed number system looks like:
4 2 1 0.5 0.25 0.125

Question 5

How are negative numbers stored?

Answer 5

Twos complement

Question 6

How is two’s complement calculated out on a denary number?

Answer 6

1. Convert the number to its binary equivalent
2. Starting from the LSB copy all bit up to and including the first 1
3. Invert all other bits after this (1s become 0s vice versa)
4. Convert the MSBs denary value to a negative

Question 7

What are the rules for addition in binary?

Answer 7

Layout the two numbers in a table with one above the other
0+0=0
1+0=1
1+1=0 carry 1 to next bits
1+1+1 carry=1 carry 1 to next bits

Question 8

How do you subtract in binary?

Answer 8

Convert the number you are subtracting into a negative twos complement number and add it to the other number. Check that the resulting binary is the correct number.

Question 9

How do you multiply in binary?

Answer 9

Place both number in a table (one above the other)
At each nought int he bottom number write all noughts in the corresponding row.
When you come to a one, copy the entire binary number above, writing its LSB starting at the position of the one.

Question 10

Describe repeated division by 2