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Understanding Sequential and Combinatorial Components in Digital Circuits

This comprehensive guide explores the intricacies of sequential and combinatorial components in digital circuits, discussing flip-flops, clocking, memory elements, and more. Learn about asynchronous and synchronous circuits, types of flip-flops, and how to implement different functionalities using various components. Dive into the world of sequential logic and understand the fundamental concepts through practical examples.

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Understanding Sequential and Combinatorial Components in Digital Circuits

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  1. Sequential Logic • Combinatorial components: the output values are computed only from their present input values. • Sequential components: their output values are computed using both the present and past input values. • Sequential circuits can contain only a finite number of states finite state machines • Synchronous and Asynchronous

  2. Sequential Circuits • Contains Memory Elements • Asynchronous sequential circuits change their state and output values when input changes • Synchronous sequential circuits change their output values at fixed points of time, which are specified by the rising or falling edge of a clock signal • Clock period is the time between successive transitions in the same direction • Active high – state changes occur at the clock’s rising edge( on higher voltage) • Active low – state changes occur at the clock’s falling edge( on lower voltage)

  3. 4 Basic types of Flip-Flops • SR, JK, D, and T • JK ff has 2 inputs, J and K need to be asserted at the same time to change the state • D ff has 1 input D (DATA), which sets the ff when D = 1 and resets it when D = 0 • T ff has1 input T (Toggle), which forces the ff to change states when T = 1 • SR ff has 2 inputs, S (set) and R (reset) that set or reset the output Q when asserted

  4. Gated D-Latch • Ensures S and R inputs never equal to 1 at the same time • Useful in control application where setting or resetting a flag to some condition is needed • Stores bits of information • Constructed from a gated SR latch and a Data latch

  5. D Flip-Flop Q+ = Next State Characteristics : Synchronous Avoids the instability of RS flip-flop Retains its last input value To set the ff, place 1 on D input and pause the CK input To reset, place 1 on D input and pause the CK input

  6. JK – Flip Flop J – Set K – Reset J = K = 0 – output does not change J = K = 1 – invert the outputs

  7. Clocked JK – Flip Flop

  8. T Flip-Flop T = 1 force the state change T = 0 state remain the same

  9. D and JK Flip-Flop

  10. How to use JK to implement D Flip-Flop D ff’s property: When in = 0, the out(Q+) = 0. When in = 1, the out(Q+) is 1   invert K   invert K D

  11. How to use JK to implement T Flip-Flop T ff’s property: When in = 0, the out(Q+) = no change When in = 1, the out(Q+) is = complement  No change  State change T

  12. How to use D to implement JK Flip-Flop (Q ) = no state change (Q’) = state change D = JQ’ + K’Q

  13. How to use D to implement JK Flip-Flop D = JQ’ + K’Q J K

  14. How to use T to implement JK Flip-Flop T = KQ + JQ’

  15. How to use T to implement JK Flip-Flop T = KQ + JQ’

  16. How to use D to implement T Flip-Flop D = TQ’ + T’Q

  17. How to use D to implement T Flip-Flop D = TQ’ + T’Q T

  18. How to use T to implement D Flip-Flop T = DQ’ + D’Q

  19. How to use T to implement D Flip-Flop T = DQ’ + D’Q D

  20. SR-Flip Flop SET RESET SET RESET

  21. SR-Flip Flop • Asynchronous • If S=0 and R=1, Q is set to 1, and Q’ is reset to 0 • IF R=0 and S=1, Q is reset to 0, and Q’ is set to 1 • If S=1 and R=1, Q and Q’ maintain their previous state • If S=0 and R=0, a transition to S=1, R=1 will cause oscillation

  22. Clocked SR Flip-Flop Similar to SR Flip-flop but with extra control input C, which enables or disables the operation of S and R inputs. C=1 Enabled C=0 Disabled, circuit persists in preceding state

  23. Instability • RS flip-flops can become unstable if both R and S are set to 0 • All sequential elements are fundamentally unstable under certain conditions • Invalid transitions • Transitions too close together • Transitions at the wrong time

  24. Edge and level-triggered Flip Flop • Digital circuit often form loops, flip-flops oscillations can • Oscillation will not occur because by the time an output change cause an input change, the activating edge of the CK signal will be gone • Positive edge triggered – ff responds to a positive going edge of clock • Negative edge triggered – responds to a negative-going edge

  25. Positive-edge-triggered D Flip-Flop When CLK=0 the master latch is open and the content of D is transferred to QM When CLK=1 the master is closed and its output is transferred to the slave Master and slave latches are never enabled at the same time

  26. References • www.play-hookey.com/digital • www.infopad.eecs.berkeley.edu/~icdesign/SLIDES/slides6.pdf • www.cs.mun.ca/~paul/cs3724/material/web/notes/node14.html • Dos Reis, Assembly Language and Computer Architecture Using C++ and Java

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