Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > Let R1 and R2 be two 4-bit registers that sto...
Start Learning for Free
Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?
- a)R1 = 1011 and R2 = 1110
- b)R1 = 1100 and R2 = 1010
- c)R1 = 0011 and R2 = 0100
- d)R1 = 1001 and R2 = 1111
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let R1 and R2 be two 4-bit registers that store numbers in 2’s c...
Stored numbers in registers R1 and R2 are in 2's complement form. Register size is 4 bits. The range of numbers in 2's complement form is -8 to +7. If R1 + R2, the result is out of the above range, then it is overflow.
The given data,
Given two four-bit registers R1 and R2.
Option 1: R1 = 1011 and R2 = 1110
False,
R1 = 1 0 1 1 = -(0101)= -5
+ R2 = 1 1 1 0 = -(0010)= -2
-----------------------------------------------
The given data,
Given two four-bit registers R1 and R2.
Option 1: R1 = 1011 and R2 = 1110
False,
R1 = 1 0 1 1 = -(0101)= -5
+ R2 = 1 1 1 0 = -(0010)= -2
-----------------------------------------------
1 0 0 1 = = -7
Here No overflow occurred, because sign bit is same for (R1 + R2 ).
Option 2: R1 = 1100 and R2 = 1010
True,
R1 = 1 1 0 0 = -(0100)= -4
+ R2 = 1 0 1 0 = -(0110)= -6
Option 2: R1 = 1100 and R2 = 1010
True,
R1 = 1 1 0 0 = -(0100)= -4
+ R2 = 1 0 1 0 = -(0110)= -6
--------------------------------------------
0 1 1 0 = = -10
Here Overflow occurred because the sign bit is different for (R1 + R2 ).
Option 3: R1 = 0011 and R2 = 0100
False,
R1 = 0 0 1 1 = +(0011)= +3
+ R2 = 0 1 0 0 = +(0100)= +4
Option 3: R1 = 0011 and R2 = 0100
False,
R1 = 0 0 1 1 = +(0011)= +3
+ R2 = 0 1 0 0 = +(0100)= +4
--------------------------------------------
0 1 1 1 = +7
Here No overflow occurred, because the sign bit is the same for (R1 + R2 ).
Option 4: R1 = 1001 and R2 = 1111
False,
R1 = 1 0 0 1 = -(0111) = -7
+ R2 = 1 1 1 1 = -(0001) = -1
Option 4: R1 = 1001 and R2 = 1111
False,
R1 = 1 0 0 1 = -(0111) = -7
+ R2 = 1 1 1 1 = -(0001) = -1
--------------------------------------------
1 0 0 0 = = -8
Here No overflow occurred, because the sign bit is the same for (R1 + R2 ).
Hence the correct answer is R1 = 1100 and R2 = 1010.
Here No overflow occurred, because the sign bit is the same for (R1 + R2 ).
Hence the correct answer is R1 = 1100 and R2 = 1010.
Most Upvoted Answer
Let R1 and R2 be two 4-bit registers that store numbers in 2’s c...
's complement representation. Let's denote the numbers stored in R1 and R2 as N1 and N2, respectively. In 2's complement representation, the leftmost bit represents the sign of the number, with 0 indicating a positive number and 1 indicating a negative number.
To add N1 and N2, we can use the following steps:
1. Check the sign bit of N1 and N2. If they have different signs, we need to perform subtraction instead of addition. If they have the same sign, we can proceed with addition.
2. If N1 and N2 have different signs, we need to find the absolute values of N1 and N2 and perform subtraction. To find the absolute value of a negative number in 2's complement representation, we can invert all the bits and add 1 to the result.
3. Perform addition or subtraction of the absolute values of N1 and N2, taking into account the carry generated from the previous bit.
4. If there is a carry-out from the most significant bit, it indicates overflow, which means the result cannot be represented in the given number of bits. In this case, we need to handle the overflow.
5. If the result is negative, we need to convert it back to 2's complement representation by inverting all the bits and adding 1 to the result.
6. Store the result in a separate register, which we can call R3.
Note that these steps assume that the numbers in R1 and R2 are properly aligned, meaning that their sign bits are in the same position. If they are not aligned, additional steps may be required to align them before performing addition or subtraction.
To add N1 and N2, we can use the following steps:
1. Check the sign bit of N1 and N2. If they have different signs, we need to perform subtraction instead of addition. If they have the same sign, we can proceed with addition.
2. If N1 and N2 have different signs, we need to find the absolute values of N1 and N2 and perform subtraction. To find the absolute value of a negative number in 2's complement representation, we can invert all the bits and add 1 to the result.
3. Perform addition or subtraction of the absolute values of N1 and N2, taking into account the carry generated from the previous bit.
4. If there is a carry-out from the most significant bit, it indicates overflow, which means the result cannot be represented in the given number of bits. In this case, we need to handle the overflow.
5. If the result is negative, we need to convert it back to 2's complement representation by inverting all the bits and adding 1 to the result.
6. Store the result in a separate register, which we can call R3.
Note that these steps assume that the numbers in R1 and R2 are properly aligned, meaning that their sign bits are in the same position. If they are not aligned, additional steps may be required to align them before performing addition or subtraction.
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Similar Electronics and Communication Engineering (ECE) Doubts
Top Courses for Electronics and Communication Engineering (ECE)View all
Top Courses for Electronics and Communication Engineering (ECE)
Question Description
Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer?.
Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer?.
Solutions for Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?a)R1 = 1011 and R2 = 1110b)R1 = 1100 and R2 = 1010c)R1 = 0011 and R2 = 0100d)R1 = 1001 and R2 = 1111Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
|
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily