Sequential Logic. (Materials taken from: Principles of Computer Hardware by Alan Clements )

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Sequential Logic

(Materials taken from: Principles of Computer Hardware by

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Sequential vs. Combinational

Circuits

• Combinatorial circuits: their outputs are

computed entirely from their present inputs

• Sequential circuits: their outputs are

computed using both the present input and

their previous output

– The idea of a next state

– A clock input triggers the transition from the current state to next state.

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Sequential Logic Elements

• Sequential logic can perform as many different functions as combinational logic

• Certain functions have been given names. – Latch: a 1-bit memory element

– Register : m latches in a row and is able to store an m-bit word

– Shift register: special-purpose register that moves the bits of the word left or right

– Counter: special-purpose register that when triggered (i.e. clocked) increases its contents by 1

– State machines: moves from one state to another each time it is triggered

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The Flip-Flop

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Analysis by Assuming Initial

Conditions

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Clocked RS Flip-Flop

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D Flip-Flop

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D Flip-Flop Chip

2 active low inputs called preset and clear - Unconditional

- Set high in normal usage - Used on power-up

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Registers

Registers transmit and receive data from buses Flip-flops are clocked to latch the data

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Registers

The most common sequential building block is the register. A register is N bits wide and has a load line for loading in a new value into the register.

Note that DFF simply loads old value when LD = 0. DFF

i l d d l k l

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Ways of Clocking a Flip-Flop

• A clocked flip-flop captures a digital value and

holds it; three ways of clocking:

1. Whenever the clock is asserted (i.e. a level-triggered flip-flop).

2. Whenever the clock is changing state (i.e. an edge-triggered flip-flop).

3. Capture data on one edge of the clock and

transfer it to output on the following edge (i.e. a master–slave flip-flop)

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Level-Triggered FF

• The type of FF we have discussed so far

• Not appropriate for all applications

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Edge-Triggered FF

• An edge-triggered flip-flop is clocked not by

the level of the clock (i.e. high or low), but by

the transition of the clock signal from zero to

one, or one to zero.

– Positive or rising-edge sensitive – Negative or falling-edge sensitive

– The rising or falling edge of a pulse can have durations less than 1 ns

– Like an level-sensitive clock triggered by a infinitesimally short pulse

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Edge-Triggered FF

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Edge-Triggered FF

• Variation in the arrival time of clock pulses to

FF clock inputs is called clock skew

• Caused by differences in the paths by which

clock pulses reach flip-flops

– Distance

– Temperature – Age

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JK Flip-Flop

Edge-triggered flip-flops

When a JK flip-flop is

clocked, it behaves like an RS flip-flop (where J = S, K = R) for all input

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Summary

• Flip-flops have internal state as well as

external inputs---they are memory elements

• The most common forms of flip-flop are: D

flip-flop, RS flip-flop, and JK flip-flop

• Flip-flops have two outputs: Q and Q

• Most flip-flops are clocked and the clock is

used to trigger the flip-flop.

• Flip-flops often have unconditional preset and

clear inputs used the set or clear the output

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Shift Register

• Shift register: bits can be moved one place right every time the register is clocked

• Example, the binary pattern 01110101

becomes 00111010 after the shift register is clocked once

and 00011101 after it is clocked twice

and 00001110 after it is clocked three times, and so on

• After the first shift a 0 has been shifted in from the left-hand end and the 1 at the right-left-hand end has been lost

• Shifting 1 place right has the effect of dividing the number by 2; 1 place left corresponds to multiplying by 2

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Shift Register

Very useful sequential building block Used to perform either Very useful sequential building block. Used to perform either parallel to serial data conversion or serial to parallel data

conversion.

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Counter

Very useful sequential building block. Used to generate memory y q g g y addresses, or keep track of the number of times a datapath

operation is performed.

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