3. For each of the specifications below give a state machine for the sequential circuit. Be sure to o minimize the number of states in your machine o draw the state diagram, and o identify the initial state. a. (5 points) Design a state machine that recognizes the sequences 1100 or 0010 on a synchronous input, x. That is, your state machine should have one output signal which is high only when the last 4 inputs (including the current input) are 1100 or 0010. The first four outputs can be either zero or one since the circuit's output will be ignored until four inputs have been given. Note that the two sequences can overlap with each other and themselves. The output (z) is shown below for a sequence of inputs (x) x 01 00101 1 00 1 0 0 0 001011 1 0 0011 11 . . z ? ? 0 0 1 00 01 0 1 0 0 0 00 1 00 00 1 0 0 0 00 .. . b. (5 points) Design a state machine with one input and one output. The output should be 1 whenever there are three 1s followed by an even length block of Os and the current input is 1. (A block of Os is a group of one or more consecutive inputs that are low.) Below is a sample sequence of inputs and the corresponding outputs. input 11 0 0 111001 111 0 000100111 00011 1 010111 .- output 0000 0000010 000 0001 0000000000 0 00 0000.. 5 points Design a state machine which has two inputs, bl and b0, and one output, z The inputs bl and b0 represent a binary number from 0 to 3 The output z should be 1 whenever the value of (b1,b0) is either 1, 2 or 3 and the past 1,2 or 3 inputs, respectively, have been 00. That is, the output is high when the value of (b1,b0) is n for n>0 and the past n inputs have been 0,0The output z is shown below for a sequence of inputs b D. he va e v of bo sa s s own e ow to llustrate the operation; it is not an output.) ? bi 0 011 0 0 0 0 11 1 1 0 01 0 000 1 1 0 0 1 0 0 0 0 0 00 01... b0 0 111 0000111 1 0 0 01 0 1 001 0111 0 01 00 0 0 0 z 0 1000 00 01000001 00 1 0 0001000 010000 1.. v 0 13 300 0 03 333 0 0210 1 0 2 301310 0 10 0002.. . 3. For each of the specifications below give a state machine for the sequential circuit. Be sure to o minimize the number of states in your machine o draw the state diagram, and o identify the initial state. a. (5 points) Design a state machine that recognizes the sequences 1100 or 0010 on a synchronous input, x. That is, your state machine should have one output signal which is high only when the last 4 inputs (including the current input) are 1100 or 0010. The first four outputs can be either zero or one since the circuit's output will be ignored until four inputs have been given. Note that the two sequences can overlap with each other and themselves. The output (z) is shown below for a sequence of inputs (x) x 01 00101 1 00 1 0 0 0 001011 1 0 0011 11 . . z ? ? 0 0 1 00 01 0 1 0 0 0 00 1 00 00 1 0 0 0 00 .. . b. (5 points) Design a state machine with one input and one output. The output should be 1 whenever there are three 1s followed by an even length block of Os and the current input is 1. (A block of Os is a group of one or more consecutive inputs that are low.) Below is a sample sequence of inputs and the corresponding outputs. input 11 0 0 111001 111 0 000100111 00011 1 010111 .- output 0000 0000010 000 0001 0000000000 0 00 0000.. 5 points Design a state machine which has two inputs, bl and b0, and one output, z The inputs bl and b0 represent a binary number from 0 to 3 The output z should be 1 whenever the value of (b1,b0) is either 1, 2 or 3 and the past 1,2 or 3 inputs, respectively, have been 00. That is, the output is high when the value of (b1,b0) is n for n>0 and the past n inputs have been 0,0The output z is shown below for a sequence of inputs b D. he va e v of bo sa s s own e ow to llustrate the operation; it is not an output.) ? bi 0 011 0 0 0 0 11 1 1 0 01 0 000 1 1 0 0 1 0 0 0 0 0 00 01... b0 0 111 0000111 1 0 0 01 0 1 001 0111 0 01 00 0 0 0 z 0 1000 00 01000001 00 1 0 0001000 010000 1.. v 0 13 300 0 03 333 0 0210 1 0 2 301310 0 10 0002
