# Output z depends on the input x and on the state of

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Output z depends on the input x and on the state of the memory (A,B)

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Analysis D D x A A A B B clk z x x Next state Logic Output Logic memory The memory has 2 FFs and each FF can be in state 0 or 1. Thus there are four possible states: AB: 00,01,10,11. Output z depends on the input x and on the state of the memory (A,B) To describe the behavior of a sequential circuit, we need to show 1. How the system goes from one memory state to the next as the input changes 2. How the output responds to input in each state
D D x A A A B B clk z x x Next state Logic Output Logic memory Analysis of Sequential Circuits . . ; . ; ( ). A B D A x B x D A x z A B x

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D D x A A A B B clk z x x Next state Logic Output Logic memory Analysis of Sequential Circuits . . ; . ; ( ). A B D A x B x D A x z A B x ( 1) ( ). ( ). ( 1) ( ). ( ). A t A t x B t x B t A t x z A B x
D D x A A A B B clk z x x Next state Logic Output Logic memory Analysis of Sequential Circuits Present State Input Next State A B A B x z 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 Output State Transition Table 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 . . ; . ; ( ). A B D A x B x D A x z A B x ( 1) ( ). ( ). ( 1) ( ). ( ). A t A t x B t x B t A t x z A B x

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D D x A A A B B clk z x x Next state Logic Output Logic memory Present State Input Next State A B A B x z 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 Output State Transition Table 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0
D D x A A A B B clk z x x Next state Logic Output Logic memory 00 Memory state in which FF A& B have output values 00 Present State Input Next State A B A B x z 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 Output State Transition Table 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0

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D D x A A A B B clk z x x Next state Logic Output Logic memory 00 Memory state in which FF A& B have output values 00 00 x=0/z x=1/z ? ? If x = 0 then z = 0, When the clock edge comes the system would stay in 00 state. If x = 1 then z = 0. When the clock edge comes the system would go to 01 state. Present State Input Next State A B A B x z 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 Output State Transition Table 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0
D D x A A A B B clk z x x Next state Logic Output Logic memory 00 Memory state in which FF A& B have output values 00 00 x=0/z x=1/z ? ? If x = 0 then z = 0, When the clock edge comes the system would stay in 00 state. If x = 1 then z = 0. When the clock edge comes the system would go to 01 state. 00 0/0 01 1/0 Present State Input Next State A B A B x z 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 Output State Transition Table 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0

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D D x A A A B B clk z x x Next state Logic Output Logic memory Analysis of Sequential Circuits
D D x A A A B B clk z x x Next state Logic Output Logic memory Analysis of Sequential Circuits ( 1) ( ). ( ).

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