Question

In this problem, you will design a 4-bit 2's complement negator (without overflow detection). Every four cycles, the machine will take in 4 1-bit values x 0 ​ ,x 1 ​ ,x 2 ​ ,x 3 ​ (in order from LSB to MSB, where x 0 ​ is input for cycle n,x 1 ​ is input for cycle n+1, etc.) and produce 41 1-bit values y 0 ​ ,y 1 ​ ,y 2 ​ ,y 3 ​ (in order from LSB to MSB, where y 0 ​ is output for cycle n,y 1 ​ is output for cycle n+1, etc.) such that y 3:0 ​ =−x 3:0 ​ . Every four cycles after reset, a new four bit value begins. Let the input bit be x and the output bit be y. (a) Draw a transition diagram for the Mealy implementation, minimizing the number of states. (b) Using the minimum necessary number of D flip-flops, set the state encoding and derive SoP expressions for the next state and output logic.

Answer 1

The transition diagram for the Mealy implementation of the 4-bit 2's complement negator is designed by considering the states and inputs. State encoding can be implemented using 4 D flip-flops, and SoP expressions can be derived for the next state and output logic.

Step-by-step explanation:

Transition Diagram

The transition diagram for the Mealy implementation of the 4-bit 2's complement negator can be designed by considering the states and inputs. Since there are 4 bits, we can have a total of 16 different states. Each state represents a particular combination of bits. The inputs x0, x1, x2, and x3 represent the values in each cycle. The outputs y0, y1, y2, and y3 represent the negated values of x0, x1, x2, and x3 respectively.

State Encoding and SoP Expressions

To implement the negation, we can use a combinational logic circuit with 4 inputs and outputs. The state encoding depends on the number of bits required to represent the states. In this case, we need 4 D flip-flops to store the current state, so we will use a 4-bit binary encoding. The next state and output logic can be derived using sum-of-products (SoP) expressions based on the desired behavior and inputs.