1. Consider the adder-subtractor circuit shown in Figure 3-31. Suppose the 4-bit inputs
   A₃ A₂ A₁ A₀ and B₃ B₂ B₁ B₀ are unsigned binary numbers. In other words, the decimal equivalents of the input values are 0, 1, ..., 15. The circuit will add the inputs if S = 0 and subtract B from A when S = 1.

   Design a circuit that will convert the output C₄ S₃ S₂ S₁ S₀ to the corresponding number in 5-bit signed magnitude representation. In addition, you should detect when overflow errors occur.

   Your circuit should output 6 binary values: V to indicate overflow, 1 sign bit G, and 4 bits
   M₃ M₂ M₁ M₀ for the magnitude. You can assume that full adders are available for use in your circuit, as well as other logic gates (AND, OR, NOT, etc.).

   You may find it useful to begin by considering some particular input values and finding the desired outputs from your circuit. What is the range of output values that can be achieved with no overflow? How will you detect overflow?

2. Again consider the adder-subtractor circuit shown in Figure 3-31. Now suppose that the 4-bit inputs A₃ A₂ A₁ A₀ and B₃ B₂ B₁ B₀ are in signed 2's complement format. In other words, the decimal equivalents of the input values are -8, -7, ..., +7.

   Design a circuit to perform the same operation described in question 1. You may find it useful to begin by considering some particular input values and finding the desired outputs from your circuit. What is the range of output values that can be achieved with no overflow? How will you detect overflow?

3. Optional excercise: (we won't discuss in class)

   Design a binary multiplier that multiplies two 4-bit numbers (this is called a 4-bit by 4-bit multiplier). Use 4-bit binary adders and AND gates in your design. Show the complete logic circuit diagram.

Thank you.