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Sequential Logic Computer Organization Ellen Walker Hiram College Figures from Computer Organization and Design 3ed, D.A. Patterson & J.L. Hennessey, Morgan Kauffman © 2005 unless otherwise specified

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Sequential Logic Combinational logic “forgets” its results when the inputs are no longer available Sequential logic “remembers” results until the next clock signal

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A Memory Cell ~Q = 0 (or 1) Q = 1 (or 0)

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A Settable Cell Replace NOT with NOR 0 NOR Q = ~Q –As before 1 NOR Q = 0 –Set / reset cell

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Truth Table for SR Latch RSQ~Q 00Q’~Q’ 0110 1001 11??

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Clock Signal Periodic alternation between 0 and 1 Does not have to be evenly divided Example: One period Rising edgeFalling edge

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Clocked D Latch CDQ~Q 00Q’~Q’ 01Q’~Q’ 1001 1110

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Action of D Latch D C Q

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Latch vs. Flip Flop Latch changes by level –As long as C is high, Q follows D Flip flop changes by edge –Q takes value of D at rising (or falling) edge only

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D Flip-Flop with Falling Edge Trigger When C is high, “master” follows D When C is low, “slave” follows Q of “master” When C is low, Q of “master” is locked in.

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Action of D Flipflop D C Q

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Setup and Hold Time Setup time: Minimum time D must be stable before clock edge Hold time: Minimum time D must be stable after clock edge

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Determining Clock Cycle Combinational logic must be done before D needs to be stable Therefore, (combinational logic + setup time + hold time) < clock cycle

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Other Flip Flops T (toggle): When T is set, flip-flop changes value at clock edge JK (very general ff) –When J=K=1, toggles at edge –When J=1, K=0, sets at edge –When J=0, K=1, resets at edge –When J=K=0, holds value

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Counter from T Flip Flops Low Order Bit: –T=1, clock = external signal Each additional bit: –T=1, clock = Q from lower bit –When lower bit falls, higher bit toggles Delay increases as # bits increase (“ripple effect”)

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Sequential Circuit Allows Feedback Combinational Logic D C Q External inputs Clock signal

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Register from D Flip Flops One register is simply a set of D flip- flops, one per bit Data inputs are D’s Data outputs are Q’s and ~Q’s Clocks all tied together

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Register File Several registers grouped together To read: –Input = register # –Output = register data To write: –Inputs = register #, register data, clock (write signal) –Output = (none)

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Implementing Read Ports

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Implementing Write Ports

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4x2 DRAM from D-FFs

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State Machine Sequential logic holds state Combinational logic computes new state and output (based on old state)

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Graphical Representation

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Building a State Machine Determine the states and transitions Assign numbers to the states –If there are N states, you need log N flip flops to hold the state number Create “next state” logic Create “output” logic

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Example: Parity Checker One input, which sequentially gets the bits of a word One output, 0 if number of 1’s since reset is even, 1 if number of 1’s since reset is odd Asynchronous reset sets parity back to 0

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Pattern Recognizer Input: Sequence of Bits Output: –If last 2 bits were “10” output is 1 –If bit pattern “111” is found, output is 0 and remains 0 no matter what –Otherwise, output is 0

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