Question

11001 in binary system corresponds to following number in decimal system

• A. 25
• B. 20
• C. 30
• D. 15

Hint:

To quickly convert binary to decimal, just write down the powers of 2 (1, 2, 4, 8, 16, 32, ...) from right to left above the binary digits and add up the powers of 2 where the binary digit is a '1'. For 11001: {ccccc} 16 & 8 & 4 & 2 & 1
1 & 1 & 0 & 0 & 1
Sum = 16 + 8 + 1 =

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question requires the conversion of a number from the binary (base-2) system to the decimal (base-10) system. In the binary system, each digit's place value is a power of 2.

Step 2: Key Formula or Approach:
To convert a binary number to decimal, you multiply each binary digit by its corresponding place value (a power of 2) and then sum up all the results. The place values start from \(2^0\) for the rightmost digit and increase to the left.
For the binary number \(11001_2\):

• The rightmost digit '1' is in the \(2^0\) position.
• The next digit '0' is in the \(2^1\) position.
• The next digit '0' is in the \(2^2\) position.
• The next digit '1' is in the \(2^3\) position.
• The leftmost digit '1' is in the \(2^4\) position.

Step 3: Detailed Explanation:
We can write the conversion as follows:
\[ (11001)_2 = (1 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) \] Now, calculate the value of each term:
\[ = (1 \times 16) + (1 \times 8) + (0 \times 4) + (0 \times 2) + (1 \times 1) \] \[ = 16 + 8 + 0 + 0 + 1 \] \[ = 25 \] So, the decimal equivalent of the binary number 11001 is

Step 4: Final Answer:
The binary number 11001 corresponds to 25 in the decimal system.