1110.1101 plus 110101.01101 what the binary number system addition?

Answer 1

Addition in binary works exactly the same way as addition in decimal. The only difference between the two is the number of digits one has to work with. In the case of decimal we have ten digits, and in binary we have two.

Recall that in regular decimal addition, we do a special operation when the digits we add together are greater than our largest single digit, "9". For example:

''''5

+7

-----

12

(*note that the ' character is being used for spacing, as this wiki automatically trims white spaces)

If you consider this carefully, what we're doing is taking sum of the two values, dividing them by ten, and making the result our first digit, and the remainder our second digit. Addition is done the same way, but with two instead of ten:

'''''1

+ 1

------

10

To add the given binary numbers in your question then, you would do it like so:

'''''''''1110.1101

+110101.01101

-------------------------

First, fill out the empty decimals on the left with more zeroes;

''''''''1110.11010

+110101.01101

-------------------------

Now, go through each of the digits from right to left, adding them together and carrying the digits over where applicable:

'''111111 1

'''''''''1110.11010

+110101.01101

-------------------------

1000100.00111