Q8: Unsigned Arithmetic#

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

Objective
Reinforce an understanding of unsigned arithmetic.

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