The following picture is a block diagram of an arithmetic unit dedicated to IEEE 754 floating-point addition from Computer Organization and Design RISC-V Edition: The Hardware Software Interface 2nd Edition book.

My questions are:

  1. Why are in the sketch, the sign of the numbers ignored, while the final result has a sign bit?
  2. In the IEEE 754 standard, there is a hidden '1' bit for normalized numbers. How does this bit take part in addition?

enter image description here

  • $\begingroup$ Please ask only one question per post. If you have two questions, you can post them separately. $\endgroup$
    – D.W.
    Commented Dec 29, 2023 at 21:26

1 Answer 1


Hidden leading bit: You add a 1 when you extract the mantissa except for denormalised numbers where you add zero.

You use both sign bits to determine whether you add the mantissas (same sign) or subtract (different signs). And the result of the sign comes from the sign of the bigger number.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.