Question

**Adder**

Start out by picking 2 positive six bit binary numbers that are
less than 32_{10}, written in 2's complement notation. The
eventual goal is to add these two numbers.

1) Look at the LSB bit of the numbers, and using logic gates (NANDs, NORs, etc.) design a circuit that correctly gives the right output for any possible combination of bits in the LSB place.

2) Now look at the next column to the left (next to LSB). In this column we must both add the bits, and deal with a potential carry bit from the LSB. Modify your circuit to add correctly when there is a carry bit, and to output both the correct answer and a carry bit. [Hint; circuit will have 3 inputs (2 number bits plus a carry bit) and 2 outputs (answer and a carry bit).

3) For each of the logical elements in problem 2, write down the corresponding CMOS transistor circuits. [You don't need to wire all of the bits together, just show the transistor circuits for each logical gate.]

4) Redraw the answer from 2 into a new functional block (3 in, 2 out), the 1 bit adder. [Show inputs and outputs, but hide internal operation.] Using your new functional block, build a 6 bit adding circuit.

**Other Arithmetic Units**

5) Build a circuit that converts a positive 6 bit integer into a negative number

6) Reusing the adder from 4), build a subtractor.

7) Build a circuit that can shift bits one bit to the left.

8) Sketch out a circuit that can multiply two 6 bit numbers. Explain your logic and how the circuit would function. [Drawing out the full circuit is optional.]

Answer #1

Implement a 2-bit adder using only a 32x3 ROM. The adder adds
two 2-bit numbers, {A1 A0} and {B1 B0}. The adder also has a
carry-in (Cin) input. Thus there are 5 inputs: A1 A0, B1 B0, Cin.
There are 3 outputs, a 2-bit sum (S1 S0) as well as a carry-out
(Cout). Include a diagram of the ROM: label inputs/outputs
correctly and show the contents of ROM cells (0's/1's).

Design a 4-bit adder-subtractor circuit using the 4-bit binary
Full adders (74LS83) and any necessary additional logic gates. The
circuit has a mode input bit, M, that controls its operation.
Specifically, when M=0, the circuit becomes a 4-bit adder, and when
M=1, the circuit becomes a 4-bit subtractor that performs the
operation A plus the 2’s complement of B.Where A and B are two
4-bits binary numbers. That is,
* When M=0, we perform A+B, and we assume that
both...

Design a combinational circuit that forms the 2-bit binary sum
S1S0 of two 2-bit numbers X1X0 and Y1Y0 and can produce a carry
output C. Design the entire circuit with the help of three half
adder circuit implementing each of the three outputs with XOR-AND
and OR gates.

The software I am using Is Logisim.
Design and build a circuit to add 2 2-bit binary numbers. This
means that you will have 4 input lines and 3 output lines. The
three output lines are 2 bits for the sum and a carry out line. Use
logisim to construct your circuit. Upload the .circ file to
blackboard

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