Question

Design a circuit to compute: f=x²+y+2 in which x,y are 2-bit inputs, f is output.

Draw the circuit to implement this circuit. Please write down your design steps (only 3 steps: specification, formulation and optimization).

Answer 1

The design steps for creating a digital circuit to compute f=x²+y+2 include specification, formulation into a logic diagram, and optimization to reduce complexity. A combination of logical gates and adders would be used to achieve the function.

Step-by-step explanation:

Design Steps for a Circuit Computing f=x²+y+2

The question involves designing a digital circuit to compute the function f=x²+y+2, where x and y are 2-bit inputs, and f is the output. The design steps are as follows:

1. Specification: Establishing the requirements of the circuit. In this case, it's to compute the function f=x²+y+2 using binary numbers as inputs for x and y.
2. Formulation: Translating the function into a logic diagram using AND, OR, NOT, and XOR gates, along with any needed adders. Since x is squared, a mini circuit for squaring the binary input will be part of the design.
3. Optimization: Simplifying the circuit where possible to reduce the number of gates and therefore, complexity and cost. This may involve combining gates using Boolean algebra optimization techniques.

In the digital design, squaring a 2-bit number can be achieved with AND gates for the fixed 1-bits in the binary multiplication, and XOR gates could be used for the addition part. An adder circuit would be necessary for summing the final binary numbers. Unfortunately, as I cannot draw the circuit here, this description will guide you on setting it up.