3. Consider a sequential circuit that reads in an input X(t) during clock cycle t. The circuit should look for the sequence 011. Design the sequential circuit (i.e., give simplified algebraic expressions) using D flip-flops for each of the following versions: (a) If the second 1 arrives during clock cycle t, then the circuit should output a 1 during clock cycle t, and otherwise outputs a 0. (b) If the second 1 arrives during clock cycle t, then the circuit should output a 1 during the clock cyclet+1, and otherwise outputs a o. (c) Suppose the sequence is 111 instead of 011. If at time t, the current and two previous inputs were a then a 1 should be output during clock cycle t, and otherwise a O should be output. Note that multiple consecutive outputs of 1 are possible