Convert the following floating point binary number to a decimal number.
The mantissa is:
The exponent is:
Step 1: Calculate the exponent value
The exponent is:
The first value is , which means the exponent is .
Work Out The Complement
Because the exponent is negative, we need to work out the complement.
Flip the bits and add 1
So the complement is
Convert to denary
We can convert the exponent to denary in the normal way, which gives us .
Step 2: Determine if the mantissa is positive or negative
The mantissa is:
The first number is , which means the mantissa is .
Work Out The Complement
Because the exponent is negative, we need to work out the complement.
Flip the bits and add 1
Gives us…
Step 3: Move the point to the correct position
On a normalised floating point number, the point goes between the first and second bit.
The exponent has a value of , which is a number, so the point moves places to the .
If we need more digits to the left, we can pad with zeroes if it is a positive mantissa, or ones if it is a negative mantissa.
Step 4: Covert to decimal
We can now convert our binary number back to denary. This is done in the usual way, remembering that numbers to the right of the point are fractions.
Step 5: Remember to add the sign back in
The mantissa is negative, so remember to put that negative symbol back onto our denary answer.
And we're done!