Binary Floating Point Addition

Question

How does 1.000(base2) x 2^-1 + (-0.111(base2) x 2^-1) = .001(base2) x 2^-1? To add binary numbers don't you simply just add? I'm not seeing how the addition works..

Answer 1

I'm not sure what you mean when you ask "don't you simply just add?", but the math is correct. It is basically in base-2 scientific notation.

1.000(base2) x 2^-1 = 0.100(base2)
-0.111(base2) x 2^-1 = -0.0111(base2)

0.100 + (-0.0111) = 0.0001

0.0001 = 0.001(base2) x 2^-1

Answer 2

Things are a lot more complicated with floating point numbers. Let's start with integers.

To turn a positive number into a negative, you invert all the bits and add one. This is called "two's complement" arithmetic. -0111 becomes 11111001 if we use 8-bit numbers for our example.

Now when you add up the numbers, 00001000+11111001=100000001 . The overflow from the upper-most bit gets thrown away, leaving you with 00000001 .