The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15C...
Decimal to Binary Conversion
To understand the decimal equivalent of the given binary number (1101)2, we need to convert it into decimal form. The binary number system uses only two digits, 0 and 1, while the decimal number system uses ten digits, 0 to 9.
Binary to decimal conversion involves multiplying each binary digit by powers of 2 and then adding up the results. Starting from the rightmost digit, the powers of 2 increase from right to left, with the rightmost digit having a power of 2^0, the second rightmost digit having a power of 2^1, the third rightmost digit having a power of 2^2, and so on.
Conversion Steps
To convert the binary number (1101)2 to decimal, follow these steps:
1. Start from the rightmost digit of the binary number.
2. Multiply each binary digit by the corresponding power of 2.
3. Add up the results obtained in step 2 to get the decimal equivalent.
Calculation Process
Let's calculate the decimal equivalent of the binary number (1101)2 using the conversion steps described above:
(1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= (1 * 8) + (1 * 4) + (0 * 2) + (1 * 1)
= 8 + 4 + 0 + 1
= 13
Therefore, the decimal equivalent of the binary number (1101)2 is 13.
Conclusion
The correct answer is option 'C' - 13. By following the conversion steps for binary to decimal conversion, we determined that the decimal equivalent of the binary number (1101)2 is 13.
The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15C...
Step by step solution:
- Step 1: Write down the binary number: 1101
- Step 2: Multiply each digit of the binary number by the corresponding power of two: 1x23 + 1x22 + 0x21 + 1x20
- Step 3: Solve the powers: 1x8 + 1x4 + 0x2 + 1x1 = 8 + 4 + 0 + 1
- Step 4: Add up the numbers written above: 8 + 4 + 0 + 1 = 13
- So, (1101)2 = (13)10