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.
Then add them all together.

Question 10

Describe repeated division by 2

Question 11

Describe the process of finding the denary value from a FLOATING POINT mantissa exponent

Answer 11

1. Convert the exponent to denary
2. Move the decimal point from between the MSB and the second MSB depending on this value
3. Convert to denary

Question 12

How to convert a number from denary to mantissa exponent

Answer 12

1. Convert to binary
2. If negative convert to twos complement
3. When putting in the mantissa place the point between the first 1&0
4. The exponent is how many places the decimal place was moved from its original position to do this

Question 13

Name two benefits of normalisation

Answer 13

Ensures greatest degree of accuracy
Reduces likelihood of errors as system is standardised