Question

Decimal number 10 is equivalent to binary number _______?

a) 1010
b) 1110
c) 1001
d) 1111

Answer 1

The decimal number 10 is equivalent to the binary number 1010. This is determined by converting the decimal number to binary through successive division by 2 and recording the remainders, then reversing the order of the remainders to get the binary representation.

Step-by-step explanation:

The decimal number 10 is equivalent to the binary number 1010. To convert a decimal number to binary, you divide the number by 2 and write down the remainder, repeating this process with the quotient until you get a quotient of 0. Here are the steps for converting the decimal number 10 to binary:

1. Divide 10 by 2, which equals 5 with a remainder of 0. Hence, the last digit (least significant bit) is 0.
2. Divide 5 by 2, which equals 2 with a remainder of 1. So the next digit is 1.
3. Divide 2 by 2, which equals 1 with a remainder of 0. So the next digit is 0.
4. Finally, 1 divided by 2 is 0 with a remainder of 1. So the first digit (most significant bit) is 1.

Writing these remainders in reverse order (from most significant to least significant bit) gives us the binary number 1010. Therefore, the correct answer is a) 1010.