Problem of 1’s Complement Representation

1. Two Zeros Exist
• Positive Zero: 0000
• Negative Zero: 1111
? This creates ambiguity, because logically both are zero but they have different bit patterns.

2. End-Around Carry Needed
When adding numbers, if a carry comes out of the MSB, it must be added back to the LSB.
(+5) = 0101
(-5) = 1010   (1’s complement of 0101)
----------------
Add: 1111 → End-around carry = 1
Final: 0000 (after adding carry)
? Result is zero, but note that two different zeros are possible.

3. Hardware Complexity
Extra logic is required so that +0 and -0 are treated the same, making design slower and costlier.

✅ Conclusion

That’s why modern systems use 2’s complement. It has only one zero and simplifies arithmetic operations.