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ECE-200 Digital Logic Design Homework 8 Problem 1 Design a sequential circuit with one input x and one output F that detects the sequence 1101 (specifically, a 1 followed by a 1, followed by a 0, followed by a 1). When the sequence is detected, your circuit should produce a 1 on the output F; otherwise, it should produce 0. Implement your design as a Mealy Finite State Machine (FSM). You may assume your state register is initialized to contain all 0’s when powered on. Design your sequential circuit so that it does not allow for overlapping sequences. For example, if the input sequence 11101101 is provided to your circuit over eight sequential clock ticks, your circuit should output a 1 on F when the fourth 1 is received but not when the sixth 1 is received. (3 pts) Define the states needed to implement this system and draw the State Transition Diagram.
Problem 1 (continued) (3 pts) Draw the State Transition Table using the variable names for your states (i.e. Sp, S1, etc). (3 pts) Assign binary representations to your states and redraw the State Transition Table using these binary state representations.
Problem 1 (continued) (5 pts) Write the equation for the output circuit (F) and the “next-state” equations for the state transition circuit. Use “don’t cares” from any unused states and K-Maps to produce sum-of-products expressions that use the fewest logic gates possible.
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Problem 2 A sequential circuit has one input x and one output F. The output F is 1 if and only if x has been 1 for exactly three consecutive clock ticks. Note that if we receive 111 over three ticks, we will need to know the next input before we can decide if the input sequence is exactly three 1’s. A snapshot of the input/output from such a system (implemented as a Moore Machine & as a Mealy Machine) is provided for clarity: P 4 X o1 111111 011011101 0 0 O Fealy o 00 0600 0 0O0O0O0OO0OO0OO0OO0OT1UO0O0O00 Foore o 00 0600 0 0O0O0O0O0OO0OO0OO0OO0OT1O0O00 Recall that the output for a Moore Machine is delayed by 1 clock tick whereas the output for a Mealy machine is not. For the following questions, you may assume your state register is initialized to contain all 0’s when powered on. (3 pts) Define the states needed to implement this system as a Mealy Machine and draw the State Transition Diagram. (3 pts) Draw the State Transition Table for your Mealy Machine using the variable names for your states (i.e. Sy, S1, etc).
Problem 2 (continued) (3 pts) Define the states needed to implement this system as a Moore Machine and draw the State Transition Diagram. (3 pts) Draw the State Transition Table for your Moore machine using the variable names for your states (i.e. Sy, S1, etc).
Problem 3 A sequential circuit has one input x and one output F. The output F is 1 if and only if x has been 1 for three consecutive clock ticks. Input sequences of 111 cannot overlap (i.e. a 1 on the input can only be used to count toward one 1 on the output). A snapshot of the input/output from such a system implemented as a Mealy Machine is provided for clarity: X o 1111 111011011101 0 00 F o 0010 0100O0O0O0O0O0O1 000 00 Recall that the output for a Moore Machine is delayed by 1 clock tick whereas the output for a Mealy machine is not. For the following questions, you may assume your state register is initialized to contain all Os when powered on. (3 pts) Define the states needed to implement this system as a Mealy Machine and draw the State Transition Diagram. (3 pts) Draw the State Transition Table for your Mealy Machine using the variable names for your states (i.e. Sy, S1, etc).
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Problem 4 A sequential circuit has one input x and one output F. The output F is 1 if and only if exactly two 1’s followed by a 0 and then a 1 are received on the input x. Input sequences may overlap. A snapshot of the input/output from such a system implemented as a Mealy Machine is provided for clarity: O | O | o Ol O < ! x 0 01 1 01101101 1 0 1 1 0 1 F 000O0UO0OT1TU0UO0T1SU0 0 1 00 1 0 0 1 Valid sequences are colored using using red and blue (alternating). 1’s shared by two overlapping valid sequences are shown in purple. An invalid sequence is highlighted by the arrows. This invalid sequence does not begin with exactly two 1’s; so, the output is 0. For the following questions, you may assume your state register is initialized to contain all 0’s when powered on. (3 pts) Define the states needed to implement this system as a Mealy Machine and draw the State Transition Diagram. Hint: Start by drawing only the states and transitions that lead to producing a 1 on the output F. This is the “success path.” Once you are confident your success path is correct, add the remaining transitions for each state — you may need to add additional states when doing this.
Problem 4 (continued) (3 pts) Draw the State Transition Table for your Mealy Machine using the variable names for your states (i.e. Sy, S1, etc). (3 pts) Give your states binary representations and redraw the State Transition Table using the binary representations.
Problem 4 (continued) (5 pts) Write the equations for the output circuit (F) and for the state transition circuit. Use “don’t cares” from unused states and K-Maps to produce sum-of-products expressions that use the fewest logic gates possible.
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Problem 4 (continued) (5 pts) Draw the complete system schematic for your circuit. 10
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