Question

In this problem, you will design a 4-bit 2's complement sub tractor, implement it in Logic works, and test it. The 4-bit sub tractor works as follows: given two numbers X and Y in 2's complement binary representation on 4 bits, it outputs a 4-bit value representing X - Y in 2's complement. To obtain full marks, the following requirements must be met: You are only allowed to use basic gates, including NOT, AND, OR, NAND, NOR, XOR, XNOR. (You can of course include connections to the ground or to the supply voltage, and additional 10 elements such hex display, hex keyboard, etc.) You should, in the course of your design, implement a 1-bit adder. Encapsulate this 1-bit full adder as a new reusable sub circuit with its own device symbol, which will be saved in a local library file (see Section 3 of the Logic works 5 reference, under "Creating a Sub circuit-Bottom-Up" for details) The final circuit should be exhaustively tested through an imported timing file (see Appendix). The testing mechanism for your design should include a comparator circuit to test whether the output from the 4-bit sub tractor you have implemented corresponds to the expected result (which can be loaded from the imported timing file). Explain and document all your steps and design choices; truth tables, Carnage maps, equations, all designed circuit diagrams and corresponding Logic works timing outputs should be included in your DOC or PDF submission, and all corresponding Logic works files should be included in your assignment submission to allow testing.

Answer 1

Solution: The 4 bit 2's complement subtractor circuit is shown below: 82 A2 B1 A1 во CO C1 FA FA FA FA $3 S1 S2 So Truth table АЗ B3 S3 C3 C4

Explanation . The A- B subtractor circuit would consists an adder with inverters kept between each data input B and corresponding input of full adder. . The input carry C0 must be equal to 1 when subtraction is erformed The operation is A B's 1's complement 1 This denotes A + B's 2's complement . For unsigned numbers, if A-B then it gives A-B. if A-B then it gives (B-A)'s 2's complement. For signed numbers, result would be A-B, provided that there is no overflow