I'm having slight confusion over two's complement. I have reviewed What is “2's Complement”?.
I'm trying to add -2 + -3 = -5. Here's my thought process:
+2 = 0010
-2 = 1110 # in twos complement
+3 = 0011
-3 = 1101 # in twos complement
1101
+1101
-----
10010 # What is this?
I know -5 is 1011 in Two's Complement. But I'm not sure what I did when I added -2 + -3 in the example above.
An explanation of the process to add -2 + -3 would be appreciated. Thank you for your assistance!
In 4 bit 2'scomplement -2 is 1110 and +3 is 0011 so
11110 carry
1110 -2
+0011 +3
----
10001 which is 0001 or simply 1 ignoring the carry in bit 5
Stepping through the process from the right to the left:
1 + 0 results in 1 with no carry
1 + 1 results in 0 with a carry of 1
1 + 0 + the carry of 1 results 0 with a carry of 1
1 + 0 + the carry of 1 results in 0 with a carry of 1
just the carry of 1 results in 1 with nothing more to carry
For reference see the Wikipedia article on 2's complement particularly the section on addition at https://en.wikipedia.org/wiki/Two%27s_complement#Addition. There are a number of online 2's complement calculators to help with conversions and one of them is at http://www.exploringbinary.com/twos-complement-converter/
Let me know if you want to see how -3 + -3 is done, since that is what you attempted. It is a similar process, but be sure start with bit length large enough to avoid overflow as determined when the leftmost two bits in the carry row have different values.
-3and-3, and the answer is11010, not what you have. So it is-6- the correct answer for that sum.