Task 29

Normalise these two positive numbers :

a) 0000 0001 0100 0111.

Mantissa : 0000 0001 01
Decimal : 0.000000101
Decimal : 0.101000000

Exponent : 000111 = 7 in denary.
To get back to the original we must move the decimal point 6 places to the left.
So, I subtract 6 from the current exponent.
The new Exponent becomes : 000001

Putting this back together, I get :
0101000000000001

b) 0000 0111 0000 1011

Mantissa : 0000 0111 00
Decimal : 0.000011100
Decimal 0.111000000

Exponent : 001011 = 11 in denary.
To get back to the original mantissa, we must move the decimal place 4 places to the left.
Therefore, I need to subtract 4 from the Exponent, leaving me with 7.
The new Exponent : 000111

Putting this back together, I get :

0111000000000111