Computer Arithmetic Part-VI

[Music] let's now take a look at floating point multiplication and division the floating point multiplication is along the same lines as floating point addition and subtraction a little bit of a difference nothing much but floating point division is different so let's first take a look at floating point multiplication which is easy so

let me motivate by showing an example in decimal so let's assume that we have this convention that any you know decimal significant will be other form X point some numbers some digits and this there is basically one digit to the left of the decimal point so this will actually be four point zero

you can actually draw that so this is the convention that we are using we can multiply two numbers of the type 4.0 times let's say 10 to the power minus 4 times 5.0 times 10 to the power minus 5 so what we would do is that first we will multiply the two significance 4 and

5 so this will give us 20 point 0 and then what we will do is that we will multiply these two you know exponent terms so we will basically add the exponents and add minus 4 and minus 5 so what we will get is

twenty point zero times ten to the power minus nine so note that after the multiplication the result here that was obtained by multiplying the significance is not in the normal form so to bring it to the normal form what we can do is that we can do to make it 2.0 times ten times

ten raised to power minus 9 which is 2.0 times 10 raised to the power minus 8 so then this comes back to the normal form so we will do something very very similar with binary numbers over here so what we will do is that will add the exponents right so because it's a multiplication