To determine whether any of the given operations would result in arithmetic overflow, we must convert the 4-bit two's complement binary numbers to their decimal values and then perform the operation. An overflow occurs when the result of an addition or subtraction operation is outside the range that can be represented with the given number of bits.
In a 4-bit two's complement system, numbers range from -8 to +7.
Step 1: Convert the binary numbers to decimal
- \(N1 = 1011 \rightarrow \text{Decimal: } -5\) (as the most significant bit is 1, indicating a negative number)
- \(N2 = 1101 \rightarrow \text{Decimal: } -3\)
- \(N3 = 1010 \rightarrow \text{Decimal: } -6\)
- \(N4 = 1001 \rightarrow \text{Decimal: } -7\)
Step 2: Perform the operations
- \(N1 + N2\): \(-5 + (-3) = -8\). Within range, no overflow.
- \(N2 + N3\): \(-3 + (-6) = -9\). This is outside the range, thus resulting in overflow.
- \(N3 - N4\): \(-6 - (-7) = 1\). Within range, no overflow.
- \(N1 + N4\): \(-5 + (-7) = -12\). This is also outside the range, thus resulting in overflow.
Conclusion: The operations \(N2 + N3\) and \(N1 + N4\) both result in arithmetic overflow.
Important Questions from Number Representation
Which of the following pairs of octal and binary numbers are NOT equal?
The greatest negative number which can be stored in a 8-bit register using 2's complement arithmetic is
Which of the following codes is also known as reflected binary code?
What is the octal equivalent of (F3B1)16?
The 1's complement of binary number 10010 is
