0195136047.pdf

290 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS

(c)

01

11

10

00

00 01 11

AB

CD 10

1 11 d CD⋅

1 d

d

d

d

d

BC⋅

AD⋅ (d)

01

11

10

00

00 01 11

AB

CD 10

C

d

d

d

d

d

d

00

0

0

0

0

BD⋅

Figure E6.1.12Continued

(b) The prime implicants (with 0 cells) for the complement ofFare marked in Figure

E6.1.12(d). The minimum POS expression is then given by

F ̄=C+B ̄·D

Complementing both sides of this equation and using DeMorgan’s rules, one obtains

F=C ̄·(B+D) ̄

Note in particular that in Figures E6.1.12(c) and (d) we did not form subcubes that covered onlyds.

Sequential Blocks

Neglecting propagation delays, which are measures of how long it takes the output of a gate to

respond to a transition at the input of the gate, the output of a logic block at a given time depends

only on the inputs at that same time. The output of asequentialblock, on the other hand, depends

not only on the present inputs but also on inputs at earlier times. Sequential blocks have thus a

kind of memory, and some of them are used as computer memories.

Most sequential blocks are of the kind known asmultivibrators, which can bemonostable

(the switch remains in only one of its two positions),bistable(the switch will remain stable in

either of its two positions), andunstable(the switch changes its position continuously as a kind

of oscillator, being unstable in both of its two states). The most common sequential block is the

flip-flop, which is a bistable circuit that remembers a single binary digit according to instructions.

Flip-flops are the basic sequential building blocks. Various types of flip-flops exist, such as the

SR flip-flop (SRFF), D flip-flop (or latch), and JK flip-flop (JKFF), which differ from one another

in the way instructions for storing information are applied.

SR FLIP-FLOP(SRFF)

The symbol for the SRFF is shown in Figure 6.1.17(a), in whichSstands for “set,”Rstands for

“reset” on the input side, and there are two outputs, the normal outputQand the complementary

outputQ ̄. The operation of the SRFF can be understood by the following four basic rules.

1. IfS=1 andR=0, thenQ=1 regardless of past history. This is known as theset
   condition.


2. IfS=0 andR=1, thenQ=0 regardless of past history. This is known as thereset
   condition.


3. IfS=0 andR=0, thenQdoes not change and stays at its previous value. This is a
   highly stableinput condition.


4. The inputsS=1 andR=1 are not allowed (i.e., forbidden) becauseQQ ̄=11;Q ̄is
   no longer complementary toQ. This is an unacceptable output state. Such a meaningless