# Adding/Subtracting in binary and hexadecimal formats?

I have two numbers(in decimal):

M = 3892.74
N = 9341.65


I am trying to add and subtract them in binary numbers and then in hexadecimal numbers. I manage to convert the numbers into binary/ hexadecimal with 4 fraction digits.

M = 111100110100.1011   and M = f34.bd70
N = 10010001111101.1010 and N = 247d.a666


and I have found M + N = 13234.51 = 11001110110010.0101 = 33b2.83d6 I am having trouble doing the M - N ? Is there negative numbers in alternate number systems and how would I carry out this subtraction ? If my earlier work can be verified, I would also appreciate it. Thanks

• If you're doing this by hand, you can just put a negative sign in front like you normally would with decimal numbers. – Greg d'Eon Feb 5 '15 at 3:06
• Use binary 2's complement to make one of the numbers negative, then subtract by adding the 2's complement. – MarkU Feb 5 '15 at 4:04

M - N can be done in the usual way as:

  00111100110100.1011 -
10010001111101.1010
---------------------
1 10101010110111.0001
---------------------


We have a borrow here. Answer is negative and is in 2's complement form.

Or you can add the 2's complement of N with M.

-N = 2's complement of N = 101101110000010.0110

0 00111100110100.1011 +
1 01101110000010.0110
---------------------
1 10101010110111.0001
---------------------


Take the 2's complement of this number to get -01010101001000.1111 = -5448.9375.