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P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is
- a)111101
- b)110101
- c)110010
- d)111001
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
P, Q, and R are the decimal integers corresponding to the 4-bit binary...
Given, binary number 1100
1's complement of 1100 = -3
Sign magnitude of 1100 = -4
2's complement of 1100 = -4
∴ P + Q + R = - 4 - 3 - 4 = - 11
The 6 digit 2’s complement of (-11) = 110101
1's complement of 1100 = -3
Sign magnitude of 1100 = -4
2's complement of 1100 = -4
∴ P + Q + R = - 4 - 3 - 4 = - 11
The 6 digit 2’s complement of (-11) = 110101
Most Upvoted Answer
P, Q, and R are the decimal integers corresponding to the 4-bit binary...
In signed magnitude representation, the leftmost bit (most significant bit) represents the sign of the number. If it is 0, the number is positive, and if it is 1, the number is negative. The remaining bits represent the magnitude (absolute value) of the number.
For the 4-bit binary number 1100, the leftmost bit is 1, which means the number is negative. The remaining bits (100) represent the magnitude of the number.
To convert this to decimal, we first need to find the value of the magnitude. The rightmost bit represents 2^0, the next bit to the left represents 2^1, the next bit represents 2^2, and so on. So:
1 1 0 0
| | | |
| | | +-- 2^0 = 1
| | +---- 2^1 = 2
| +------ 2^2 = 4
+-------- 2^3 = 8
So the magnitude of the number is:
1 * 8 + 1 * 4 + 0 * 2 + 0 * 1 = 12
Since the number is negative, we simply put a minus sign in front:
-12
So P = -12.
For Q and R, we need to consider the two's complement representation. To find the two's complement of a number in signed magnitude representation, we first invert all the bits (change 1s to 0s and vice versa), and then add 1 to the result.
For the 4-bit binary number 1100, the inverted bits are:
0 0 1 1
Adding 1 to this gives us:
0 1 0 0
So the two's complement representation of -12 is 100.
To convert this to decimal, we first need to determine the value of the leftmost bit. In two's complement representation, the leftmost bit represents -2^(n-1), where n is the number of bits. So for a 4-bit number, the leftmost bit represents -8.
The remaining bits represent the magnitude of the number, just like in signed magnitude representation. So:
1 0 0
| | |
| | +-- 2^0 = 1
| +---- 2^1 = 2
+------ 2^2 = 4
So the magnitude of the number is:
1 * 4 + 0 * 2 + 0 * 1 = 4
Adding the value of the leftmost bit (-8) gives us:
-8 + 4 = -4
So Q = -4.
For R, we need to consider the one's complement representation. To find the one's complement of a number in signed magnitude representation, we simply invert all the bits (change 1s to 0s and vice versa).
For the 4-bit binary number 1100, the inverted bits are:
0 0 1 1
So the one's complement representation of -12 is 0011.
To convert this to decimal, we first need to determine the value of the leftmost bit. In one's complement representation, the leftmost bit represents -2^(n-1), where n is the number of bits. So for a 4-bit number, the leftmost bit represents -8
For the 4-bit binary number 1100, the leftmost bit is 1, which means the number is negative. The remaining bits (100) represent the magnitude of the number.
To convert this to decimal, we first need to find the value of the magnitude. The rightmost bit represents 2^0, the next bit to the left represents 2^1, the next bit represents 2^2, and so on. So:
1 1 0 0
| | | |
| | | +-- 2^0 = 1
| | +---- 2^1 = 2
| +------ 2^2 = 4
+-------- 2^3 = 8
So the magnitude of the number is:
1 * 8 + 1 * 4 + 0 * 2 + 0 * 1 = 12
Since the number is negative, we simply put a minus sign in front:
-12
So P = -12.
For Q and R, we need to consider the two's complement representation. To find the two's complement of a number in signed magnitude representation, we first invert all the bits (change 1s to 0s and vice versa), and then add 1 to the result.
For the 4-bit binary number 1100, the inverted bits are:
0 0 1 1
Adding 1 to this gives us:
0 1 0 0
So the two's complement representation of -12 is 100.
To convert this to decimal, we first need to determine the value of the leftmost bit. In two's complement representation, the leftmost bit represents -2^(n-1), where n is the number of bits. So for a 4-bit number, the leftmost bit represents -8.
The remaining bits represent the magnitude of the number, just like in signed magnitude representation. So:
1 0 0
| | |
| | +-- 2^0 = 1
| +---- 2^1 = 2
+------ 2^2 = 4
So the magnitude of the number is:
1 * 4 + 0 * 2 + 0 * 1 = 4
Adding the value of the leftmost bit (-8) gives us:
-8 + 4 = -4
So Q = -4.
For R, we need to consider the one's complement representation. To find the one's complement of a number in signed magnitude representation, we simply invert all the bits (change 1s to 0s and vice versa).
For the 4-bit binary number 1100, the inverted bits are:
0 0 1 1
So the one's complement representation of -12 is 0011.
To convert this to decimal, we first need to determine the value of the leftmost bit. In one's complement representation, the leftmost bit represents -2^(n-1), where n is the number of bits. So for a 4-bit number, the leftmost bit represents -8
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P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. Can you explain this answer?
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P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. 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 P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. Can you explain this answer?.
P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. 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 P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. Can you explain this answer?.
Solutions for P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) isa)111101b)110101c)110010d)111001Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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