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The 2’s complement representation of the decimal value - 15 is
- a)1111
- b)11111
- c)111111
- d)10001
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The 2’s complement representation of the decimal value - 15 isa)...
The 2’s complement of negative numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero
+15 = 0 1 1 1 1
The 2’s complement representation of the decimal value -15 is
-15 in 2’s complement = 10001
+15 = 0 1 1 1 1
The 2’s complement representation of the decimal value -15 is
-15 in 2’s complement = 10001
Most Upvoted Answer
The 2’s complement representation of the decimal value - 15 isa)...
Understanding 2's Complement
2's complement is a method for representing signed integers in binary form. It allows for easy arithmetic operations and is widely used in computer systems.
Steps to Find 2's Complement Representation of -15
1. Determine the Binary Representation of Positive 15
- The binary representation of 15 in 4 bits is:
- 15 = 1111
2. Invert the Bits
- Change all 0s to 1s and all 1s to 0s:
- 1111 becomes 0000
3. Add 1 to the Inverted Bits
- Now, add 1 to the inverted result:
- 0000 + 0001 = 0001
4. Final Result
- Thus, the 2's complement of -15 in 4 bits is:
- 0001
Choosing the Correct Bit Length
To represent -15 correctly using 5 bits, we follow the same steps:
1. Binary Representation of 15 in 5 bits
- 15 = 01111 (5 bits)
2. Invert the Bits
- 01111 becomes 10000
3. Add 1 to the Inverted Bits
- 10000 + 00001 = 10001
Conclusion
Therefore, the 2's complement representation of the decimal value -15 is:
- 10001 (in 5 bits).
This confirms that the correct answer is option 'D'.
2's complement is a method for representing signed integers in binary form. It allows for easy arithmetic operations and is widely used in computer systems.
Steps to Find 2's Complement Representation of -15
1. Determine the Binary Representation of Positive 15
- The binary representation of 15 in 4 bits is:
- 15 = 1111
2. Invert the Bits
- Change all 0s to 1s and all 1s to 0s:
- 1111 becomes 0000
3. Add 1 to the Inverted Bits
- Now, add 1 to the inverted result:
- 0000 + 0001 = 0001
4. Final Result
- Thus, the 2's complement of -15 in 4 bits is:
- 0001
Choosing the Correct Bit Length
To represent -15 correctly using 5 bits, we follow the same steps:
1. Binary Representation of 15 in 5 bits
- 15 = 01111 (5 bits)
2. Invert the Bits
- 01111 becomes 10000
3. Add 1 to the Inverted Bits
- 10000 + 00001 = 10001
Conclusion
Therefore, the 2's complement representation of the decimal value -15 is:
- 10001 (in 5 bits).
This confirms that the correct answer is option 'D'.
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The 2’s complement representation of the decimal value - 15 isa)1111b)11111c)111111d)10001Correct answer is option 'D'. Can you explain this answer?
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