Assume each choice below shows the addition of two 6-bit fixed-point binary numbers. Mark every choice that results in overflow. FYI: Be certain; Canvas deducts points for incorrect choices.
Group of answer choices

 0111.01
+0001.10

 0011.00
+0110.00

 1010.11
+0101.11

 0110.01
+1101.11

 1010.01
+1110.01


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.

Assume each choice below shows the addition of two 6-bit fixed-point binary numbers. Mark every choice that results in overflow. FYI: Be certain; Canvas deducts points for incorrect choices.
Group of answer choices

0111.01
+0001.10

0011.00
+0110.00

1010.11
+0101.11

0110.01
+1101.11

1010.01
+1110.01

Learn how to detect overflow in binary addition with 6-bit fixed-point numbers. This problem covers key concepts like two's complement, fixed-point representation, and signed binary arithmetic. Suitable for high school students, Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation