1. Magnitude Comparator
Dr. Ahmed Telba

2. Integrated Circuits
An integrated circuit is a piece (also called a chip) of silicon on which multiple gates or transistors have been embedded
These silicon pieces are mounted on a plastic or ceramic package with pins along the edges that can be soldered onto circuit boards or inserted into appropriate sockets

3. Integrated Circuits
SSI, MSI, LSI: They perform small tasks such as addition of few bits. small memories, small processors
 VLSI Tasks: - Large memory - Complex microprocessors, CPUs

4. An SSI chip contains independent NAND gates

5. Examples of Combinational Circuits
a) Decoders
b) Encoders
c) Multiplexers
d) Demultiplexers
E) Magnitude Comparator

6. Decoder Accepts a value and decodes it Consists of:
Output corresponds to value of n inputs
Consists of:
Inputs (n)
Outputs (2n , numbered from 0  2n - 1)
Selectors / Enable (active high or active low)

7. The truth table of 2-to-4 Decoder

8. 2-to-4 Decoder

9. 2-to-4 Decoder

10. The truth table of 3-to-8 Decoder1

11. 3-to-8 Decoder

12. 3-to-8 Decoder with Enable

13. 2-to-4 Decoder: NAND implementation
Decoder is enabled when E=0 and an output is active if it is 0

14. 2-4 Decoder with 2-input and Enable

15. Decoder Expansion Decoder expansion
Combine two or more small decoders with enable inputs to form a larger decoder
3-to-8-line decoder constructed from two 2-to-4-line decoders
The MSB is connected to the enable inputs
if A2=0, upper is enabled; if A2=1, lower is enabled.

16. Decoder Expansion

17. Combining two 2-4 decoders to form one 3-8 decoder using enable switch
The highest bit is used for the enables

18. Combinational Circuit Design with Decoders
Combinational circuit implementation with decoders
A decoder provide 2n minterms of n input variables
Since any Boolean function can be expressed as a sum of minterms, one can use a decoder and external OR gates to implement any combinational function.

19. Combinational Circuit Design with Decoders
Example Realize F (X,Y,Z) = Σ (1, 4, 7) with a decoder:

20. 1 bit Digital comparator

21. 4-bit Magnitude Comparator

22. BCD to 7-Segment Display Decoder
As we saw in the previous tutorial, a Digital Decoder IC, is a device which converts one digital format into another and one of the most commonly used device for doing this is called the Binary Coded Decimal (BCD) to 7-Segment Display Decoder. 7-segment LED (Light Emitting Diode) or LCD (Liquid Crystal Display) type displays, provide a very convenient way of displaying information or digital data in the form of numbers, letters or even alpha-numerical characters.
Typically 7-segment displays consist of seven individual coloured LED’s (called the segments), within one single display package. In order to produce the required numbers or HEX characters from 0 to 9 and A to F respectively, on the display the correct combination of LED segments need to be illuminated and BCD to 7-segment Display Decoders such as the 74LS47 do just that.
A standard 7-segment LED display generally has 8 input connections, one for each LED segment and one that acts as a common terminal or connection for all the internal display segments. Some single displays have also have an additional input pin to display a decimal point in their lower right or left hand corner.
In electronics there are two important types of 7-segment LED digital display.
1. The Common Cathode Display (CCD) – In the common cathode display, all the cathode connections of the LED’s are joined together to logic “0″ or ground. The individual segments are illuminated by application of a “HIGH”, logic “1″ signal to the individual Anode terminals.
2. The Common Anode Display (CAD) – In the common anode display, all the anode connections of the LED’s are joined together to logic “1″ and the individual segments are illuminated by connecting the individual Cathode terminals to a “LOW”, logic “0″ signal.

23. BCD to 7-Segment Display Decoder

24. 74LS47 for common-anode LED types

25. Truth Table for 7 Segment display

28. 4-to-2 Bit Binary Encoder

29. Priority Encoder
The Priority Encoder solves the problems mentioned above by allocating a priority level to each input.
The priority encoders output corresponds to the currently active input which has the highest priority. So when an input with a higher priority is present, all other inputs with a lower priority will be ignored.
The priority encoder comes in many different forms with an example of an 8-input priority encoder along with its truth table shown below.

33. 3-8 Binary Decoder with Enable

35. 2-to-4 Line NAND Binary Decoder Logic Diagram

36. De multiplexer

38. Magnitude comparator