Understanding Decimal to Binary Conversion for Number 9

Converting a decimal number to its binary equivalent is a fundamental concept in computer science and digital electronics. The binary number system uses only two digits, 0 and 1, whereas the decimal system uses ten digits (0-9). To convert a decimal number like 9 into its binary representation, we typically use the method of repeated division by 2.

Step-by-Step Conversion of Decimal 9 to Binary Number

Here is how we convert the decimal number 9 into its binary form using successive divisions by 2:

1. Divide the decimal number by 2 and note the remainder.
2. Divide the quotient obtained in the previous step by 2 and note the remainder.
3. Repeat this process until the quotient becomes 0.
4. The binary equivalent is obtained by writing the remainders in reverse order (from bottom to top).

Let's apply this method to the decimal number 9:

• $9 \div 2 = 4$ with a remainder of $1$ (This is the Least Significant Bit - LSB)
• $4 \div 2 = 2$ with a remainder of $0$
• $2 \div 2 = 1$ with a remainder of $0$
• $1 \div 2 = 0$ with a remainder of $1$ (This is the Most Significant Bit - MSB)

Now, collecting the remainders from bottom to top (MSB to LSB), we get: $1001$.

Therefore, the binary number for the decimal number 9 is 1001.

Comparing with Options

Let's look at the given options to find the binary number for 9:

• Option 1: 1100
• Option 2: 1001
• Option 3: 0111
• Option 4: 1011

Our calculated binary number, 1001, matches Option 2.

Revision Table: Common Decimal to Binary Conversions

Additional Information on Binary Numbers

The binary number system is a base-2 system. Each position in a binary number represents a power of 2, starting from the rightmost digit as $2^0$. For example, the binary number 1001 can be converted back to decimal as follows:

$1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0$

$= 1 \times 8 + 0 \times 4 + 0 \times 2 + 1 \times 1$

$= 8 + 0 + 0 + 1$

$= 9$

This confirms that the binary representation 1001 is indeed equivalent to the decimal number 9.