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What is the decimal equivalent of the binary number '1101'?
What is the decimal equivalent of the binary number '1101'?
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What is the decimal equivalent of the binary number '1101'?
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'1101' in binary is calculated as 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13.
Questions & Step-by-step Solutions
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Q: What is the decimal equivalent of the binary number '1101'?
Solution:
'1101' in binary is calculated as 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13.
Steps: 14
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Step 1: Write down the binary number '1101'.
Step 2: Identify the place values for each digit from right to left. The rightmost digit is 2^0, the next is 2^1, then 2^2, and finally 2^3.
Step 3: Assign the place values to each digit in '1101':
- The first '1' (from the left) is in the 2^3 place.
- The second '1' is in the 2^2 place.
- The '0' is in the 2^1 place.
- The last '1' is in the 2^0 place.
Step 4: Calculate the value of each digit by multiplying it with its place value:
- 1 * 2^3 = 1 * 8 = 8
- 1 * 2^2 = 1 * 4 = 4
- 0 * 2^1 = 0 * 2 = 0
- 1 * 2^0 = 1 * 1 = 1
Step 5: Add all the values together: 8 + 4 + 0 + 1.
Step 6: The total is 13, which is the decimal equivalent of the binary number '1101'.
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