About Decimal to Binary Formula
To convert decimal numbers to binary numbers, use the decimal to binary formula. The remainder formula can be used to convert decimal numbers to binary numbers. In this method, we divide the given decimal integer by 2 recursively and record the remainders until the quotient is 0 or 1.
Define Decimal to Binary Formula:
We will execute recursive division on the provided decimal value by 2 and note down the remainders until we obtain either 0 or 1 as the final quotient in the formula to convert decimal to binary approach. The steps for converting a decimal to a binary number using the decimal to the binary formula are listed below.
Step 1: Calculate the remainder by multiplying the provided decimal integer by two.
Step 2: Divide the quotient achieved in the previous step by two and record the remainder.
Step 3: Rep the stages above till the quotient is 0 or 1.
Step 4: This is our binary conversion of the given decimal number; write down the last quotient in line with remainders from last to first.
Example: Using decimal to binary formula, convert 29 decimal into a binary number.
Sol:
Using decimal to binary formula, we have,
Step 1: Divide the number by 2, and note down the remainder:
29 ÷ 2 gives Q1 = 14, R = 1
Step 2: Divide Q1 by 2, and note down the remainder:
14 ÷ 2 gives Q2 = 7, R = 0
Step 3: Divide Q2 by 2, and note down the remainder:
7 ÷ 2 gives Q3 = 3, R = 1
Step 4: Divide Q3 by 2, and note down the remainder:
3 ÷ 2 gives Q4 = 1, R = 1
Step 5: Write down the last quotient in line with remainders from last to the first, this is our binary conversion of the given decimal number: 11101
Answer: Hence, 29 as binary is (11101)2.