Question

In the binary number system $100 + 1011$ is equal to
A. 1000
B. 1010
C. 1110
D. 1111

Answer 1

Hint-A binary number is a number which is expressed in the base 2. It is used in digital electronics. In the binary system there are only two numbers, zero and one. The basic rules that is followed in adding binary numbers is
$0 + 0 = 0$
$0 + 1 = 1$
$1 + 1 = 10$
Using this we can add the given binary numbers. Just like addition of ordinary numbers we should start at the numbers at the right end of both the given numbers and then go step by step towards the left.

Step by step solution:
A binary number is a number which is expressed in the base 2. It is used in digital electronics. In the binary system there are only two numbers which are zero and one.
While adding binary digits we should take care of the following rules. The rules are
(1)zero added to zero gives zero. That is
$0 + 0 = 0$
(2) zero added to one or one added to zero gives one . that is,
$0 + 1 = 1$
$1 + 0 = 1$
(3) one added to one gives 10 .that is
$1 + 1 = 10$
Now let us use these rules to add the given binary number.
Let us start from the extreme right. The number on the extreme right of 100 is 0 and the number on extreme right of 1011 is 1. Therefore, zero plus one is one.$0 + 1 = 1$
Let us move on to the second last number. In 100 it is 0 and in 1011 it is 1. Thus, again we get $0 + 1 = 1$ .
The next number towards the left is 1 in 100 and 0 in 1011. Thus, their sum is $1 + 0 = 1$ . The last number on the left of 1011 is one corresponding to that there is no number in 100. Therefore, we can take that place to be 0 in hundred. So, adding $0 + 1 = 1$ . Hence, we can write the final answer as
$100 + 1011 = 1111$

So, the correct answer is option D.

Note:Just like adding normal numbers binary numbers are also added from right to left. That is the corresponding numbers in the right end are added first and then we go towards left one by one. In cases where we have $1 + 1$ then we should write 0 and give the extra one as carry over to the next number towards the left.