Overflow in binary addition occurs when the result of adding two fixed-point numbers exceeds the representable range for the given number of bits.

For a 6-bit fixed-point number, the leftmost bit is typically the sign bit (0 for positive, 1 for negative), and the rest of the bits represent the fractional or integer value. In this case, we are likely using signed binary numbers (two's complement) to represent both positive and negative numbers. This would mean the range for a 6-bit signed number is from $-16$ to $15.75$, since the first bit is the sign bit, and the rest are the magnitude.

Let's analyze each pair:

1. 0111.01

   • 0001.10
   • The sum is 1000.11. The result has a leading 1, which signifies a negative number, but both of the operands were positive, so this is an overflow.
     Overflow occurs.

2. 0011.00

   • 0110.00
   • The sum is 1001.00. Again, the result has a leading 1, signifying a negative number, but both of the operands were positive. Therefore, this is an overflow.
     Overflow occurs.

3. 1010.11

   • 0101.11
   • The sum is 10000.10. Since this is more than 6 bits, it exceeds the bit limit and causes an overflow.
     Overflow occurs.

4. 0110.01

   • 1101.11
   • The sum is 0011.10. This result is within the valid range for a 6-bit fixed-point number and there is no sign error, so no overflow occurs.
     No overflow.

5. 1010.01

   • 1110.01
   • The sum is 11000.10. This result exceeds 6 bits and hence causes an overflow.
     Overflow occurs.

Final Answer:

• Overflow occurs in:
  • 0111.01 + 0001.10
  • 0011.00 + 0110.00
  • 1010.11 + 0101.11
  • 1010.01 + 1110.01

Would you like further details or have any questions?

Related Questions:

1. How does two's complement represent negative binary numbers?
2. What is the range of values for a 6-bit fixed-point binary number?
3. How does overflow detection differ in unsigned vs signed binary numbers?
4. Can overflow happen in unsigned binary addition?
5. How does fractional binary addition work in fixed-point notation?

Tip:

When adding signed binary numbers, always check the sign of the result compared to the operands. If two positives yield a negative, or two negatives yield a positive, overflow has occurred.