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What is the binary equivalent of the decimal value 2010?

What is the binary equivalent of the decimal value 2010? Correct Answer 10100<sub>2</sub>

A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number and the maximum numbers that can be written with the given number of digits.

The Binary Number System: The binary number system with only two independent digits, 0 and 1, is a base-2 number system. All larger binary numbers are represented in terms of ‘0’ and ‘1’.

Decimal to Binary Conversion:

Step 1: Divide 20 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.

20 / 2 = 10 with 0 remainder

Step 2: Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.

10 / 2 = 5 with 0 remainder

Step 3: Repeat Step 2 above until the Whole part is 0.

5 / 2 = 2 with 1 remainder

2 / 2 = 1 with 0 remainder

1 / 2 = 0 with 1 remainder

Step 4: Write down the Remainders in reverse order to get the answer to 20 as a binary.

When we put the remainders together in reverse order, we get the answer 10100

Hence, the binary equivalent of decimal number 20 is 10100

NOTE:

The decimal number system has a base of 10 as it has 10 independent digits, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The octal and hexadecimal number systems have a radix (or base) of 8 and 16, respectively.

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