1. DIGITAL ELECTRONICS
THEME 2: Combinational Logic Circuits. Decoders, Multiplexers, De-multiplexers, Code converters.
For combinational logic the values of output functions (output signals) at particular moment of time t depend only on the values of input variables (input signals) at the same moment of time.
Combinational circuits are divided in two groups: Combinational arithmetic circuits (CACs) and Combinational Logic Circuits (CLCs).
DECODERS are CLCs which decode binary numbers and convert them in a code which has only one active output. All the rest outputs are in passive stage. The n-bit input code activates that output which number corresponds to the decimal equivalent of the input code. As a whole a decoder with n inputs has 2n outputs. The inputs are usually marked as X1, X2, X3, … and the outputs – Y1, Y2, Y3, … If the decoder has all the 2n outputs it is called a full (complete) decoder. If only a part of the outputs are necessary (that means only part of the input sets has to be decoded) the decoder is called incomplete.
According to the level of the output signals the decoders are:
direct output decoder – the active level of the output signal is “1” and the passive one is “0”. In this case only the output corresponding to the input binary set will be “1”.
inverse output decoder – the active level of the output is “0”.
The decoder has some enable inputs marked as Xp1, Xp2, … which determine the operation modes of the device. These inputs enable or disable the functions of the decoder according to the level of the logic signals at these inputs.

2. DIGITAL ELECTRONICS
Symbolic presentation and the logic circuit of 3 – bits input code complete direct output decoder

3. DIGITAL ELECTRONICS
The truth table of a 3 – bits input code complete decoder with inverse outputs IC The two enable inputs marked as Xp2 and Xp3 are combined in one, marked with Xр*.
Xр1
Xр* X2 X1 X0 Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Х 1

4. DIGITAL ELECTRONICS
Cascade connection of decoders – decoder with 5 inputs and 32 outputs

5. DIGITAL ELECTRONICS
MULTIPLEXER is a combinational logic device which switches digital information from multiple inputs marked as X1, X2, X3, … to a single output Y. The binary code combination at the control (address) inputs XA, XB, XC, … defines which one of the information inputs will be switched to the output. This is that input which number corresponds to the decimal equivalent of the binary code on the control inputs. The number of control inputs (n) defines the number of the information inputs (2n). As with the decoders the multiplexers has some enable inputs which enable or disable the functions of the device. The multiplexers may be with direct output or with an inverse one. Some devices have both of them.
DEMULTIPLEXER is a logic combinational device opposite to the multiplexer. Here the information from a single input X is switched to one of multiple outputs Y1, Y2, Y3, … The control (address) inputs XA, XB, XC, … define to which one of the outputs will be connected the input according to the decimal equivalent of the binary set, fed to them.

6. Symbolic presentation and the logic circuit of 8 – inputs multiplexer
DIGITAL ELECTRONICS
Symbolic presentation and the logic circuit of 8 – inputs multiplexer

7. DIGITAL ELECTRONICS
Cascade connection of multiplexers – 32-inputs multiplexer

8. IC decoder 74138 used as demultiplexer
DIGITAL ELECTRONICS
Some decoders are used as demultiplexers. The active level of enable inputs of these decoders must be the same as the active level of the outputs. An example is the 3-inputs decoder IC used as 8-channels demultiplexer.
IC decoder used as demultiplexer

9. DIGITAL ELECTRONICS
CODE CONVERTER is a logic combinational circuit where the input binary code is converted to another binary code on the outputs. The most popular code converters transform binary code to binary-coded decimal (BCD) or vice versa. Another often used code converters transform BCD to 7-segments code for control of digital indicators.
Notation of segments.
Decimal symbols, represented by 7-segments indicator
Code converters of binary-coded decimal (BCD) to 7-segments code

10. Connection of code converter with a 7-segments LED indicator.
DIGITAL ELECTRONICS
LED indicators are of two types: with common anode and with common cathode. The corresponding code converters are used to control the two indicators type. The code converters controlling LED indicators with common anode are IС 7446 and IC 7447, and for control of LED indicators with common cathode - IC 7448 and IC 7449.
Connection of code converter with a 7-segments LED indicator.

11. The truth table of code converter IC 7447.
DIGITAL ELECTRONICS
The truth table of code converter IC 7447.
symbol XD XC XB XА Ya Yb Yc Yd Ye Yf Yg 1 2 3 4 5 6
0/1 7 8 9