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What is the binary equivalent of the decimal number 51 if the binary equivalent of the decimal number 48 is 110000?
- a)110011
- b)110010
- c)110001
- d)110100
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the binary equivalent of the decimal number 51 if the binary e...
To find the binary equivalent of the decimal number 51, we can observe that the binary equivalent of 48 is 110000. Incrementing the binary number by 1 for the next decimal number, we get 110001 for 49, and further incrementing by 1 gives us 110010 for 50. Therefore, the binary equivalent of 51 is 110011.
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What is the binary equivalent of the decimal number 51 if the binary e...
Understanding Binary Conversion
To find the binary equivalent of the decimal number 51, we first need to understand the binary equivalent of 48, given as 110000.
Binary Representation Basics
- Binary is a base-2 numeral system using only two symbols: 0 and 1.
- Each digit represents a power of 2, starting from the rightmost digit, which is 2^0.
Starting Point: Binary of 48
- The binary representation of 48 is 110000.
- This means:
- 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0 = 48
Incrementing to 51
- To find the binary of 51, we simply add 3 to 48:
- 48 + 3 = 51
Adding 3 in Binary
1. Start with 110000 (48).
2. To add 3 (which is 11 in binary):
- Add 1 to the least significant bit (rightmost):
- 0 + 1 = 1 (no carry)
- Add 1 to the second least significant bit:
- 0 + 1 = 1 (no carry)
3. Thus, 110000 + 11 results in 110011.
Conclusion
- The binary equivalent of the decimal number 51 is 110011.
- Therefore, the correct answer is option A: 110011.
To find the binary equivalent of the decimal number 51, we first need to understand the binary equivalent of 48, given as 110000.
Binary Representation Basics
- Binary is a base-2 numeral system using only two symbols: 0 and 1.
- Each digit represents a power of 2, starting from the rightmost digit, which is 2^0.
Starting Point: Binary of 48
- The binary representation of 48 is 110000.
- This means:
- 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0 = 48
Incrementing to 51
- To find the binary of 51, we simply add 3 to 48:
- 48 + 3 = 51
Adding 3 in Binary
1. Start with 110000 (48).
2. To add 3 (which is 11 in binary):
- Add 1 to the least significant bit (rightmost):
- 0 + 1 = 1 (no carry)
- Add 1 to the second least significant bit:
- 0 + 1 = 1 (no carry)
3. Thus, 110000 + 11 results in 110011.
Conclusion
- The binary equivalent of the decimal number 51 is 110011.
- Therefore, the correct answer is option A: 110011.
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Question Description
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