Question

Reversible operation:

a). Draw and verify a reversible circuit that subtracts two 2-bit integers (x1 x2) and (x3 x4). [Hint: take the one’s complement of (x3 x4), increment it to form the two’s complement, then add (x1 x2). b). Design a reversible logic circuit to multiply two 2-bit integers to get a 4-bit integer. [Hints: use a reversible logic circuit with four input bits (x1, x0, y1, y0) and four output bits (p3, p2, p1, p0). c). Draw and verify a reversible circuit that takes two 2-bit integers and outputs their sum in a 3-bit register.

Answer 1

To subtract two 2-bit integers using a reversible circuit, take the one's complement of one integer, increment it to get the two's complement, and add it to the other integer. To multiply two 2-bit integers using a reversible logic circuit, use a 4x4 multiplier circuit. To add two 2-bit integers using a reversible circuit, simply add the integers and truncate the least significant bit.

Step-by-step explanation:

To design a reversible circuit that subtracts two 2-bit integers (x1 x2) and (x3 x4), you can follow these steps:

1. Take the one's complement of (x3 x4) by flipping each bit.
2. Increment the one's complement by adding the value 1 to obtain the two's complement.
3. Add the two 2-bit integers (x1 x2) to the two's complement to get the desired subtraction result.

To design a reversible logic circuit that multiplies two 2-bit integers and outputs a 4-bit integer, you can use a 4x4 multiplier circuit. The inputs (x1, x0, y1, y0) represent the two 2-bit integers, and the outputs (p3, p2, p1, p0) represent the 4-bit integer result.

To design a reversible circuit that takes two 2-bit integers and outputs their sum in a 3-bit register, you can simply add the two integers and truncate the least significant bit of the sum to fit the 3-bit register.