Truth table for a half adder
The truth table for the addition of two binary variables A and B can be shown below:
A
|
B
|
Sum
|
Carry
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
Multiplexing
A digital multiplexer or data selector multiplexer is a logic circuit that accepts several digital data inputs and selects one of them at a time to pass on to the output. Thus multiplexer transmits several signals on the same time. The purpose of the multiplexer is to save on the number of wires/lines needed to transmit data from multiple sources.
Multiplexer
Multiplexer circuits find numerous and varied applications in digital system. These application include data selection, data routing, operation sequencing, parallel-to, serial conversion, waveform generation and logic generation.
Multiplexer can be used to work like a logic function generator
Multiplexers can be used to implement logic function directly from a truth table. When used for this purpose the select inputs are used as the logic variables and each data input is connected permanently HIGH and LOW as necessary to satisfy the truth table.
_ _ _
Z = ABC+ABC+ABC
Figure: Logic function generator using MUXIC.
C
|
B
|
A
|
Z
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
Figure shows eight inputs multiplexer used to implement the logic circuit that satisfies the given truth table. The input variable A, B, C are connected to S0, S1, S2 respectively. According to the truth table, Z is supposed to be LOW when CBA = 0. This multiplexer input I0 should be connected LOW, Z is supposed to be LOW for CBA = 001, 100, 101 and 110. So that I1, I4, I5 and I6 should also be connected LOW. The other set of CBA conditions must produce Z = 1, and so multiplexer inputs I2, I3 and I7 are connected permanently HIGH.
Thus the function implemented by multiplexer can be algebraically expressed as:
_ _ _
Z = ABC+ABC+ABC
Difference between multiplexer and demultiplexer
A multiplexer takes several inputs and transmis one of them to output. A demultiplexer performs the reverse operation. It connects oe input to one of several outputs. The output is selected via select lines.
Uses of demultiplexer.
Demultiplexer circuits have various application in digital system. This application include serial to parallel conversion, data routing, address decoding and also logic function generation.
Function of enable inputs of a decoder
Some decoders have one or more ENABLE inputs that are used to control the operation of the decoder. For example, refer to the decoder in the figure below and visualize having a common enable line connected to a fourth input of each gate.
Segment Decoder
LCD segment
A LCD SEGMENT WILL TURN ON WHEN AN AC VOLTAGE IS APPLIED BETWEEN THE SEGMENT AND THE BACKPLANE AND WILL TURN OFF WHEN THERE IS NO VOLTAGE BETWEEN THE TWO.
Rather than generating ac signal, it is common practice to produce the required ac voltage by applying out-phase waves to the segment and backplane this illustrated in the figure (bellow) for one segment.
A 40-Hz square wave is applied to the backplane and the other input to the EX-OR is CONTROL input that will control whether the segment is ON or OFF.
Operation of an LCD
When there is no difference in voltage between a segment and the backplane, the segment is said to be non-activated (OFF). Segment d, e, f and in the figure (below) are OFF and will reflect incident light so that they appear invisible against their background. When an appropriate ac voltage is applied between the segment and backplane, the segment is activated (ON). Segment a, b, c in the figure are ON and will not reflect the incident light and thus they appear dark against their background.
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