Please show your work for all.

2. Design a finite state machine that has the following behavior: Inputs-0,1 Outputs 0,1 .The machine outputs 1 every time it detects a pattern "1010" otherwise it outputs O * Assume that overlapping patterns are allowed. (20 points) 3. Digital logic circuits (30 points, 10 each) A. Using logic gates, draw a circuit diagram to determine whether a given 8-bit twos complement number is equal to -1. The circuit should return 1 if the number is -1, else return 0. Use the shorthand notation for multiple-bit line when drawing the circuit. Assume the 8-bits of the number are 8 inputs to your circuit. (10 points) B. Using logic gates, draw a circuit diagram to determine whether a given 8-bit twos complement number is equal to zero. The circuit should return 1 if the number is zero, else return 0. Use the shorthand notation for multiple-bit line when drawing the circuit. Assume the 8-bits of the number are 8 inputs to your circuit. (10 points) C. Using logic gates, draw a circuit diagram for comparing two 8-bit numbers. The circuit should return 1 if the numbers match, else return 0. Use the shorthand notation for multiple bit line when drawing the circuit. (10 points)