Question

In the binary system the number 13 is written as _______.
A. 1011
B. 1101
C. 1010
D. 1110

Answer 1

Hint:Make use of a binary number system to solve this problem. By using a binary number system, we can write the value of 13 in binary numbers.

Complete step-by-step answer:
In the binary system, only two digits are there i.e., 0 and 1.
Binary number system is a number system with base 2, i.e. each binary place only contains a 0 or a 1.
Therefore, when we want to represent a number which is bigger than 1, we move up a place. The second place to the left of the point therefore represents 2, and continues to go up in multiples of 2 in the same way decimal does with 10.
To change a number from a decimal representation to a binary one, we can use this method:
Divide the decimal number in 2 and remember if the remainder was 1 or 0.
If the number you are left with is greater than 0, go back to 1
Take your remainders in reverse order to get your binary representation.
So for 13:
13 ÷ 2 = 6, here remainder is 1
6 ÷ 2 = 3, here remainder is 0
3 ÷ 2 = 1, here remainder is 1
1 ÷ 2 = 0, here reminder is 1
This gives us 1101.
Verification:
Let’s check the answer by adding the values:
1 lot of 2 × 2 × 2 + 1 lot of 2 × 2 + 0 lots of 2 + 1 lot of 1
= 8 + 4 + 0 + 1 = 13.
Therefore, 13 can be written as a binary system as 1101.
Hence, option (B) is correct.

Note:
The number ten in decimal form, 10, is way different than the number ten in binary form, 1010.
Binary system is a system to the base 10. Every mathematical operation can be done with binary the same as we do in a decimal system.