What is the value of the binary number 1001 in decimal?

What is the value of the binary number 1001 in decimal?

• A. 7
• B. 8
• C. 9
• D. 10

Answer: (C)

To convert the binary number 1001 to its decimal equivalent, we need to understand the binary system, which is base 2. In the binary system, each digit (bit) represents a power of 2, starting from the rightmost bit, which represents \(2^0\). In the binary number 1001: - The rightmost bit is 1, which represents \(1 \times 2^0 = 1\). - The next bit to the left is 0, representing \(0 \times 2^1 = 0\). - The next bit is also 0, representing \(0 \times 2^2 = 0\). - The leftmost bit is 1, representing \(1 \times 2^3 = 8\). Adding these values together gives: \[ 8 + 0 + 0 + 1 = 9 \] Thus, the decimal value of the binary number 1001 is 9, making the correct choice the one that represents this value. This understanding demonstrates how to convert binary numbers to decimal by evaluating the contributions of each bit based on its position.

To convert the binary number 1001 to its decimal equivalent, we need to understand the binary system, which is base 2. In the binary system, each digit (bit) represents a power of 2, starting from the rightmost bit, which represents (2^0).

In the binary number 1001:

• The rightmost bit is 1, which represents (1 \times 2^0 = 1).

• The next bit to the left is 0, representing (0 \times 2^1 = 0).

• The next bit is also 0, representing (0 \times 2^2 = 0).

• The leftmost bit is 1, representing (1 \times 2^3 = 8).

Adding these values together gives:

[ 8 + 0 + 0 + 1 = 9 ]

Thus, the decimal value of the binary number 1001 is 9, making the correct choice the one that represents this value. This understanding demonstrates how to convert binary numbers to decimal by evaluating the contributions of each bit based on its position.