Question

What is the binary equivalent of the decimal number 427​

Answer 1

How to Convert 427 to Binary

Decimal to Binary

Here I will show you step-by-step how to convert the decimal number 427 to binary.

First, note that decimal numbers use 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and binary numbers use only 2 digits (0 and 1).

As I explain the steps to converting 427 to binary, it is important to know the name of the parts of a division problem. In a problem like A divided by B equals C, A is the Dividend, B is the Divisor and C is the Quotient.

The Quotient has two parts. The Whole part and the Fractional part. The Fractional part is also known as the Remainder.

Step 1) Divide 427 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.

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

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

Step 4) Write down the Remainders in reverse order to get the answer to 427 as a binary.

Here I will show my work so you can follow along:

427 / 2 = 213 with 1 remainder

213 / 2 = 106 with 1 remainder

106 / 2 = 53 with 0 remainder

53 / 2 = 26 with 1 remainder

26 / 2 = 13 with 0 remainder

13 / 2 = 6 with 1 remainder

6 / 2 = 3 with 0 remainder

3 / 2 = 1 with 1 remainder

1 / 2 = 0 with 1 remainder

Then, when I put the remainders together in reverse order, we get the answer. The decimal number 427 converted to binary is therefore:

110101011