Design a circuit that either Adds or subtracts 3 from a 4-bit binary number N. Let the inputs N3, N2, N1, N0 represent N. The input K is a control signal. The circuit should have outputs M3, M2, M1, M0, which represent the 4-bit number M. When K=0, M=N+3. When K=1, M=N-3. Assume that the inputs for which M>11112 or M˂00002 will never occur and K is the most significant variable in the truth table. Implement your design with one 4-bit Binary Adder, one Quad 2-1 Multiplexer and NOT gates as required. a. Implement the function M3 with Two-Level NAND-NAND form. Assume that double-rail inputs are available from the source. b. Implement the functions M2 with a 5:32 decoder constructed from four 3:8 decoders with enable input E, one 2:4 decoder, and an external OR gate with a large fan-in. c. Realize the function M1 with a single 8-to-1 MUX. Take K, N3, N2 as selection inputs. d. Realize the function M0 with four three-state buffers, one 2:4 decoder, and other logic gates as required. Take N1, N0 as decoder inputs
Question
Design a circuit that either Adds or subtracts 3 from a 4-bit binary number N. Let the inputs N3, N2, N1, N0 represent N. The input K is a control signal. The circuit should have outputs M3, M2, M1, M0, which represent the 4-bit number M. When K=0, M=N+3. When K=1, M=N-3. Assume that the inputs for which M>11112 or M˂00002 will never occur and K is the most significant variable in the truth table. Implement your design with one 4-bit Binary Adder, one Quad 2-1 Multiplexer and NOT gates as required. a. Implement the function M3 with Two-Level NAND-NAND form. Assume that double-rail inputs are available from the source. b. Implement the functions M2 with a 5:32 decoder constructed from four 3:8 decoders with enable input E, one 2:4 decoder, and an external OR gate with a large fan-in. c. Realize the function M1 with a single 8-to-1 MUX. Take K, N3, N2 as selection inputs. d. Realize the function M0 with four three-state buffers, one 2:4 decoder, and other logic gates as required. Take N1, N0 as decoder inputs
Solution
This is a complex question that involves designing a digital circuit. Here's how you can approach it:
a. Implement the function M3 with Two-Level NAND-NAND form: The function M3 can be implemented using a two-level NAND-NAND form. This involves using NAND gates to implement the function. The first level of NAND gates will implement the AND operation, while the second level will implement the OR operation. Since we have double-rail inputs, we can use De Morgan's law to convert the AND-OR form to a NAND-NAND form.
b. Implement the functions M2 with a 5:32 decoder: To implement the function M2, we can use a 5:32 decoder constructed from four 3:8 decoders with enable input E, one 2:4 decoder, and an external OR gate with a large fan-in. The 3:8 decoders will decode the 3-bit inputs into 8 outputs, and the 2:4 decoder will decode the 2-bit inputs into 4 outputs. The outputs of the decoders will be connected to the inputs of the OR gate, which will produce the final output.
c. Realize the function M1 with a single 8-to-1 MUX: The function M1 can be realized using a single 8-to-1 multiplexer (MUX). The selection inputs for the MUX will be K, N3, and N2. The MUX will select one of its 8 inputs based on the value of the selection inputs and output it as M1.
d. Realize the function M0 with four three-state buffers, one 2:
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