Page 184 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 10: Clocked Sequential Circuits

Notes
Q1Q0 Q1Q0
00 01 11 10 00 01 11 10
Q2 Q2
0 S0 S1 S3′ S7′ 0 S0 S1 S3′
S2 S4′ S10′ S7′ S2 S4′ S10′

(a) (b)
We start with Figure 10.21(a) and first assign the reset state to the encoding for 0. Since, {S3’ S4’}
is both a high priority and medium priority adjacency, we make their assignments next. S3’ is
assigned 001 and S4’ is assigned 111. We assign {S7’, S10’} next because this pair also appears
in the high and medium priority lists. We assign them the encodings 010 and 110, respectively.
Besides giving them adjacent assignments this places S7 near S0, S3’, and S4’, which satisfies some
of the lower priority adjacencies.
The final adjacency is {S1, S2}. We give them the assignments 001 and 101. This satisfies a medium
priority placement as well as the lowest priority placements.
The second assignment is shown in Figure 10.21(b). We arrived at it by a similar line of reasoning,
except that we assigned S7’ and S10’ the state’s 100 and 110. The second assignment does about
as good a job as the first, satisfying all the high and medium priority guidelines as well as most
of the lowest priority ones.

Electronic Flip-Flop

he first electronic flip-flop was invented in 1918 by William Eccles and F. W. Jordan. It
was initially called the Eccles–Jordan trigger circuit and consisted of two active elements
T(vacuum tubes). Such circuits and their transistorized versions were common in
computers even after the introduction of integrated circuits, though flip-flops made from
logic gates are also common now.
Early flip-flops were known variously as trigger circuits or multivibrators. A multivibrator
is a two-state circuit; they come in several varieties, based on whether each state is stable or
not: an astable multivibrator is not stable in either state, so it acts as a relaxation oscillator; a
monostable multivibrator makes a pulse while in the unstable state, then returns to the stable
state, and is known as a one-shot; a bistable multivibrator has two stable states, and this is the
one usually known as a flip-flop. However, this terminology has been somewhat variable,
historically. For example:
• 1942 – multivibrator implies astable: “The multivibrator circuit is somewhat similar to
the flip-flop circuit, but the coupling from the anode of one valve to the grid of the other
is by a condenser only, so that the coupling is not maintained in the steady state.”
• 1942 – multivibrator as a particular flip-flop circuit: “Such circuits were known as ‘trigger’
or ‘flip-flop’ circuits and were of very great importance. The earliest and best known of
these circuits was the multivibrator.”
• 1943 – flip-flop as one-shot pulse generator: “It should be noted that an essential difference
between the two-valve flip-flop and the multivibrator is that the flip-flop has one of the
valves biased to cutoff.”
• 1949 – monostable as flip-flop: “Monostable multivibrators have also been called ‘flip-
flops’.” Contd...

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