Page 128 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Using Primitive Logic Functions to Build More Complex Functions w 109

Larger multiplexers are also common in designs: for example, 4: 1 multi-
plexers with four data inputs feeding one output and 8: 1 multiplexers with
eight data inputs feeding one output. In the case of a 4:l multiplexer, we will
require two select inputs to choose between the four data inputs (using binary
patterns of 00, 01, 10, and 11). Similarly, in the case of an 8:l multiplexer, we
will require three select inputs to choose between the eight data inputs (using
binary patterns of OOO,OOI,OIO, 011,100, 101,110, and 111).

Decoders
A decoder uses a binary value, or address, to select between a number
of outputs and to assert the selected output by placing it in its active state.
For example, consider a 2:4 (“two-to-four”) decoder (Figure 11-5).

2:4 DEC

--
--
-y
-y [3] = select [l] I select [0]
select
=
[3]
[l]
[0]
I
select
[0]
[2]
=
[I]
-y [2] = select [I] I select [0]
I
select
-y
select
-y [I] = select [I ] I select [0]
-y [0] = select [I] I select [0]
OK
Figure 11-5. A 2:4 decoder with active-low outputs
The 00,01,10 and 11 annotations on the decoder symbol represent the
possible values that can be applied to the seIect[I:0] inputs and are used to
indicate which output will be asserted.
The truth table shows that when a particular output is selected, it is
asserted to a 0, and when that output is not selected, it returns to a 1. Because
the outputs are asserted to Os, this device is said to have active-low outputs.