Decimal to Binary Conversion

Using decimal to binary formula, convert 3 decimal into a binary number. 

Using decimal to binary formula, 

Step 1: Divide the number by 3, find the remainder.

3 ÷ 2 gives Q₁ = 1, R₁ = 1

Step 2: Divide Q₁ by 2, find the remainder.

1 ÷ 2 gives Q₂ = 0, R₂ = 1

Step 3: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in the reverse order (R_n, R_{(n – 1)} …. R₁), this is the binary conversion of the given decimal number: 11

Answer: Hence, 3 as binary is (11)₂

Using decimal to binary formula, convert 5 decimal into a binary number. 

Using decimal to binary formula, 

Step 1: Divide the number by 5, find the remainder.

5 ÷ 2 gives Q₁ = 1, R₁ = 1

Step 2: Divide Q₁ by 2, find the remainder.

2 ÷ 2 gives Q₂ = 1, R₂ = 0

Step 3: Divide Q2 by 2, find the remainder.

1 ÷ 2 gives  Q3 = 0, R3 = 1

Step 4: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in the reverse order (R_n, R_{(n – 1)} …. R₁), this is the binary conversion of the given decimal number: 101

Answer: Hence, 5 as binary is (101)₂

Using decimal to binary formula, convert 8 decimal into a binary number. 

Using decimal to binary formula, 

Step 1: Divide the number by 8, find the remainder.

8 ÷ 2 gives Q₁ = 2, R₁ = 0

Step 2: Divide  Q1 by 2, find the remainder.

4 ÷ 2 gives Q₂ = 1, R₂ = 0

Step 3: Divide  Q2 by 2, find the remainder.

2 ÷ 2 gives Q₃ = 0, R₃ = 0

Step 4: Divide  Q3 by 2, find the remainder.

1 ÷ 2 gives Q₄ = 0, R₄ = 1

Step 5: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in the reverse order (R_n, R_{(n – 1)} …. R₁), this is the binary conversion of the given decimal number: 1000

Answer: Hence, 8 as binary is (1000)₂

How to convert decimal numbers to binary numbers?

1. Divide the decimal number by 2.
2. Note down the remainder (either 0 or 1) and the quotient.
3. Repeat the division process with the quotient obtained in the previous step until the quotient becomes 0.
4. Write the remainders obtained from the divisions in reverse order. These remainders form the binary equivalent of the decimal number.

How to convert decimal fraction to binary?

To convert a decimal fraction to binary, follow these steps:

1. Multiply the decimal fraction by 2.
2. Note the integer part of the result as the binary digit.
3. Take the fractional part of the result and repeat step 1.
4. Continue this process until you obtain the desired precision or until the fractional part becomes 0.

The binary digits obtained in step 2 form the binary equivalent of the decimal fraction.

How to convert point decimal to binary?

Converting a decimal number with both integer and fractional parts (point decimal) to binary involves separating the integer and fractional parts and converting each part individually.

1. Convert the integer part of the decimal number to binary using the rules mentioned earlier for converting decimal numbers to binary.
2. Convert the fractional part of the decimal number to binary using the steps outlined for converting decimal fractions to binary.
3. Combine the binary representations of the integer and fractional parts, placing the binary point (or decimal point) appropriately to form the binary equivalent of the point decimal number.

What are the rules to convert a decimal number into a binary number?

The rules to convert a decimal number to binary are as follows:

1. Start by dividing the decimal number by 2.
2. Note the remainder and quotient.
3. Repeat the division process with the quotient obtained in the previous step until the quotient becomes 0.
4. Write down the remainders obtained in reverse order. These remainders form the binary equivalent of the decimal number.

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