Q8: Unsigned Arithmetic

Time Estimate15-30 minutes   Grade Impact0.5%   DueSep 21 @ 12pm  

Objective
Reinforce an understanding of unsigned arithmetic.

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Free Response Questions

1. Why is a single half adder insufficient for Boolean addition?

2. Explain the differences between Decimal and Boolean addition.

3. When is it helpful to shift bits?

Multiple Choice Questions

4. For unsigned binary addition, overflow occurs when:

   • The sign bit changes.
   • There is a carry out of the most significant bit.
   • The most significant sum bit is 1.
   • The XOR of the two most significant carries is 1.

5. The sum output of a 1-bit full adder is:

   • $A \oplus B$
   • $A \oplus B \oplus c_\text{in}$
   • $(A \cdot B) \oplus c_\text{in}$
   • $(A \oplus B) \cdot c_\text{in}$

6. A correct expression for the carry-out ($c_\text{out}$) of a full adder is:

   • $c_\text{out} = A\cdot B + c_\text{in} \cdot (A \oplus B) $
   • $c_\text{out} = A \oplus B \oplus c_\text{in} $
   • $c_\text{out} = (A + B) \cdot c_\text{in} $
   • $c_\text{out} = (A \oplus B) + c_\text{in}$

7. Compute 4-bit unsigned addition: 0110 + 1011. Which is correct?

   • Sum = 0001, Carry-out = 1
   • Sum = 0001, Carry-out = 0
   • Sum = 1000, Carry-out = 1
   • Sum = 1000, Carry-out = 0

8. The half adder carry-out signal for input pair $(A, B)$ is HIGH when:

   • $A \cdot B = 1$
   • $A \oplus B = 1$
   • $A + B = 0$
   • $A = B$

9. What is the minimal number of gates required by a full adder?

   • 4
   • 5
   • 6
   • 7

10. When is the output of a 2-input XOR gate HIGH? Select all that apply.

    • When both inputs are HIGH
    • When neither input is HIGH
    • When exactly one input is HIGH
    • When exactly one input is LOW