# How do we do arithmetic with negative floating point numbers?

I'm studying floating point arithmetic and understand everything in the positive domain but can't seem to wrap my head around how negative floating point numbers are dealt with.

I understand that the sign bit in the 754 IEEE floating point number is the MSB of the bit representation of the number but how will a negative operand interact in terms of subtraction and in multiplication/division?

I apologize in advance if this is a trivial question or if there are resources online for this but I haven't been able to find anything that explains dealing with negative operands in a comprehensive manner.

Thank you.

In general, however, changing the sign of one of the operands in an operation on floating-point numbers has exactly the effect that it logically should have. Adding $$-x$$ to another number is exactly the same as subtracting $$x.$$ Subtracting $$-x$$ is exactly the same as adding $$x.$$ Multiplying $$-x$$ by $$-y$$ will give the same result as multiplying $$x$$ and $$y.$$ (It is possible that both results will be an overflow, but that's not a problem caused by the sign bit!)
• You don't "2s complement" a floating-point number. To change $x$ to $-x$ you just change the sign bit, and the mantissa and exponent stay the same. – David K Dec 7 '18 at 13:58