How is the decimal number 9 represented in binary?

How is the decimal number 9 represented in binary?

• A. 1000
• B. 1001
• C. 1010
• D. 1101

Answer: (B)

To represent the decimal number 9 in binary, we can use the method of successive division by 2, keeping track of the remainders. Starting with 9: 1. 9 divided by 2 gives a quotient of 4 and a remainder of 1. 2. 4 divided by 2 gives a quotient of 2 and a remainder of 0. 3. 2 divided by 2 gives a quotient of 1 and a remainder of 0. 4. 1 divided by 2 gives a quotient of 0 and a remainder of 1. Next, we read the remainders from bottom to top, which results in 1001. Thus, the binary representation of the decimal number 9 is indeed 1001. This binary number corresponds correctly to the decimal value, as each position in binary represents a power of 2: - The rightmost bit (1) represents \(2^0\) or 1. - The next bit (0) represents \(2^1\) or 0. - The next bit (0) represents \(2^2\) or 0. - The leftmost bit (1) represents \(2^3\) or

To represent the decimal number 9 in binary, we can use the method of successive division by 2, keeping track of the remainders. Starting with 9:

1. 9 divided by 2 gives a quotient of 4 and a remainder of 1.

2. 4 divided by 2 gives a quotient of 2 and a remainder of 0.

3. 2 divided by 2 gives a quotient of 1 and a remainder of 0.

4. 1 divided by 2 gives a quotient of 0 and a remainder of 1.

Next, we read the remainders from bottom to top, which results in 1001. Thus, the binary representation of the decimal number 9 is indeed 1001. This binary number corresponds correctly to the decimal value, as each position in binary represents a power of 2:

• The rightmost bit (1) represents (2^0) or 1.

• The next bit (0) represents (2^1) or 0.

• The next bit (0) represents (2^2) or 0.

• The leftmost bit (1) represents (2^3) or