GATE Exam  >  GATE Questions  >  The decimal equivalent of the binary number (... Start Learning for Free
The decimal equivalent of the binary number (1101)2 is
  • a)
    9
  • b)
    11
  • c)
    13
  • d)
    15
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
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.
Free Test
Community Answer
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
Explore Courses for GATE exam
The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer?
Question Description
The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer?.
Solutions for The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The decimal equivalent of the binary number (1101)2 isa)9b)11c)13d)15Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
Explore Courses for GATE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev