Need help with the following questions. Please show your steps so I can understand how to solve. Thank you!

Note: Please show your work as appropriate. An answer containing only the result will not earn full credit and will lose most of the points.

1. Design a combinational circuit with three inputs and one output. The output is 1 when the binary value of the inputs is an even number. The out is 0 otherwise.

2. Design a combinational circuit with three inputs, x, y, z, and three outputs, A, B, C. When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is two less than the input.

3. Design a combinational circuit that compares two 4-bit numbers to check if they are equal. The circuit output is equal to 1 if the two numbers are equal and 0 otherwise.

4. Using a decoder and external gates, design the combinational circuit defined by the following Boolean function.

F1 = xyz+xz

F2 = xyz+xy

F3 = xyz + xy