Number System


Decimal system: Although all of us are doing addition in decimal system since years and this may look a bit odd to study this again but I’ll still emphasize to study it further. Let us analyze the addition for decimal system.  For addition we firstly add least significant digits and keep the least significant digit of the result we get, in the least significant position of the sum and rest of the part is taken as carry and added to the next digits as:

But let me put it in another way which is actually a generalized method for addition. We first add least significant digits and if result we get is equal to or more that ‘10’ (base) then we’ll subtract ‘10’ (b) from the result as many times we can and remainder is then saved in the sum register while the number of times we can subtract is taken as carry.

Now we’ll take this method and apply it to any system for addition

Binary system:
There are 4 cases of addition of bit by bit:
                Sum       carry
0 + 0 =     0                0
1 + 0 =      1               0
0 + 1 =      1               0
1 + 1 =      1             1

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