CSI-2111 Computer Architecture I page 7-1

7. Sequential circuits, 2nd part

Objectives: To recognize and know to use the principal types of sequential circuits

Registers Counters Generators of imposed sequences

CSI-2111 Computer Architecture I page 7-2

Registers

Are sequential circuit capable of storing information of several bits (word).

Made of a set of flip-flops of the same type, driven by the same clock pulse.

There can be external gates to control the inputs of the flip-flops.

CSI-2111 Computer Architecture I page 7-3

4 bits Register with D flip-flops

CSI-2111 Computer Architecture I page 7-4

Registers (II)

Contents: series of bits Length: a number of flip-flops The flip-flops used usually

transition on the clock pulse (ascending or descending).

Any sequential circuit can be made up of registers!

CSI-2111 Computer Architecture I page 7-5

Registers (III)

A register preserves the state!

Combinational Circuit

Register (state)C

Inputs Outputs

Value of the next state

CSI-2111 Computer Architecture I page 7-6

Realization with register & ROM

Design the following sequential circuit using a ROM and of a register

– A1(t+1)(A1,A2,x) = A1x’

– A2(t+1)(A1,A2,x) = A2 x’

– y(A1,A2,x) = A2 x

Let us find the canonical SOP form

= m(4, 6)= m(1, 2, 5, 6)= m(3, 7)

CSI-2111 Computer Architecture I page 7-7

Realization with register & ROM

8x3 ROM and 2 bits registers (D flip-flops )

ROM8x3

D1 A1 Q1

D2 A2 Q2

C x y

0

1

2

22

21

20

CSI-2111 Computer Architecture I page 7-8

Calculation of the following state and y

Transition Table

Current State Input Next State OutputA1 A2 x A1 A2 y0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

CSI-2111 Computer Architecture I page 7-9

Calculation of next state and y

Transition Table

Current State Input Next State OutputA1 A2 x A1 A2 y0 0 0 0 0 00 0 1 0 1 00 1 0 0 1 00 1 1 0 0 11 0 0 1 0 01 0 1 0 1 01 1 0 1 1 01 1 1 0 0 1

CSI-2111 Computer Architecture I page 7-10

Programming of the ROMProgramming Table

Adresses Output22 21 20 0 1 20 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

CSI-2111 Computer Architecture I page 7-11

Programming of the ROM *Count of transition just as it is!!!

(with D flip-flops only)

Adresses Output22 21 20 0 1 20 0 0 0 0 00 0 1 0 1 00 1 0 0 1 00 1 1 0 0 11 0 0 1 0 01 0 1 0 1 01 1 0 1 1 01 1 1 0 0 1

CSI-2111 Computer Architecture I page 7-12

Several types of registers…

Shift registers– one-way (left or right-hand side)– bidirectional

Shift registers with loading– series or parallel

Built with RS, D, T, JK flip-flops … From 1, 2, 3, 4, 8, 16… N bits

CSI-2111 Computer Architecture I page 7-13

Counters

Goes through a predetermined sequence of states.

Made up of flip-flops . Useful in counting, the division of

frequency of clock, and in the generation of unspecified sequences.

CSI-2111 Computer Architecture I page 7-14

Counters (II) They have various characteristics:

– Coding binary, decimal, modulo M…

– Mode Asynchronous (ripple counter) synchronous (all on the same clock

signal)

– With loading (or not)– Self-correcting (or not)

CSI-2111 Computer Architecture I page 7-15

Additional readings

In Mano and Kime:– Sections 5.1 to 5.3: registers– Sections 5.4 to 5.6: counters– Sections 7.1 to 7.5: transfer between

registers