Your Question:

P4 (10 Points): You are given a 4-bit adder as a black box (say a microchip that you can't modify). The adder is too small for what you need to do and also does not compute an overflow bit. Draw a circuit that uses the 4-bit adder and any additional elements that you think are necessary to implement a 6-bit ripple-carry adder that also computes an overflow bit. Label all inputs, outputs and components.

Step By Step Answers with Explanation

- A 4-bit adder can only handle 4-bit inputs and produce a 4-bit output.

- We need to create a circuit that can combine two 4-bit adder outputs and calculate the overflow bit.

Step 3: Add the Lower 4 Bits

Connect the two 6-bit numbers (A[0:3] and B[0:3]) to the 4-bit adder, labeling them A0, A1, A2, A3, B0, B1, B2, and B3. The 4-bit adder's output will be a 4-bit sum (S[0:3]).

Step 6: Calculate the Overflow for the Upper Bits

To compute the overflow for the upper 2 bits, you can use the XOR gate again. Connect the Cout from the 2-input full adder to an XOR gate, with the other input set to 0 (since there is no carry-in from the lower 4 bits). The output of this XOR gate (OVL[1]) is the overflow bit for the upper 2 bits.

In summary, this circuit uses a 4-bit adder for the lower 4 bits, a 2-input full adder for the upper 2 bits, XOR gates to calculate the overflow bits, and logical connections to combine the results. This circuit enables you to perform 6-bit addition and compute overflow.