Page 91 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes
Larger decoders can be built using the sum-of-products structure in Figure 5.9 c, or else they can
be constructed from smaller decoders. Figure 5.10 shows how a 3-to-8 decoder is built with two
2-to-4 decoders. The w2 input drives the enable inputs of the two decoders. The top decoder is
enabled if w2 = 0, and the bottom decoder is enabled if w2 = 1. This concept can be applied for
decoders of any size. Figure 5.11 shows how five 2-to-4 decoders can be used to construct a 4-to-16
decoder. Because of its treelike structure, this type of circuit is often referred to as a decoder tree.
Decoders are useful for many practical purposes. We showed the sum-of-products implementation
of the 4-to-1 multiplexer, which requires AND gates to distinguish the four different valuations
of the select inputs s1 and s0. Since a decoder evaluates the values on its inputs, it can be used to
build a multiplexer as illustrated in Figure 5.11. The enable input of the decoder is not needed in
this case, and it is set to 1. The four outputs of the decoder represent the four valuations of the
select inputs.
Figure 5.11: A 4-to-16 Decoder Built using a Decoder Tree

Be careful in the manual decoding, it should be followed in all cases and each
circuit should be tested as it is completed.
We can convert a 3-to-8 decoder from two 2-to-4 decoders with enabling signals.

Combinatorial Game Theory

ombinatorial game theory (CGT) is a branch of applied mathematics and theoretical
computer science that studies sequential games with perfect information, that is,
Ctwo-player games which have a position in which the players take turns changing in
defined ways or moves to achieve a defined winning condition. CGT does not study games
with imperfect or incomplete information (sometimes called games of chance, like poker).

Contd...

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