ECE 2110: Introduction to Digital Systems Chapter 6 Combinational Logic Design Practices Decoders.

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ECE 2110: Introduction to Digital Systems Chapter 6 Combinational Logic Design Practices Decoders

2 Previous… Circuit Timing

3 Decoder Multiple-input/multiple-output device. Inputs ( n ) are less than outputs ( m ). Converts input code words into output code words. One-to-One mapping : - Each input code produces only one output code. Input codes : - Binary Code - Your Code ! Output Codes 1-out-of-m code Gray Code BCD Code enable inputs

4 Display Decoders Seven segment display for decimal digits. Consider the function for the ‘a’ (top segment) signal. How many inputs? Design the decoder:  SOP vs. POS

5 Binary Decoders n-to- 2 n decoder : n inputs and 2 n outputs. Input code : n bit Binary Code. Output code : 1-out-of- 2 n, One output is asserted for each input code. Example : n=2, 2-to-4 decoder Note “x” (don’t care input notation).

6 Binary 2-to-4 decoder

7 MSI Binary 2-to-4 decoder: 74x139 Input buffering (less load) NAND gates (faster)

8 74x139 : Logic Symbol -Truth Table G Y0 Y1 Y2 Y3 A B Active Low Enable, Active Low outputs Truth Table Logic Symbol Inputs Outputs G_L B A Y3-L Y2-L Y1-L Y0_L 1 X X G_L A B Y0_L Y1_L Y2_L Y3_L 1/2 74x139

9 Complete 74x139 Decoder

10 74x138: 3-to-8 Binary decoder

11 74x138: Logic Symbol

12 74x138: Truth Table

13 Decoders as logic function generators Advantages : - Flexibility - Multiple-output Logic functions Disadvantages : - Complexity : for large number of inputs ( 5-variable Function with 3 minterms ! F= AB’CD’E + A’BC’DE+A’BCDE’ )

14 Implementing the Canonical Sum The binary decoder generates all minterms of n-variable logic function. The canonical sum ( sum of minterms ) of a logic functions is obtained by adding all minterms of that function: -Match the order of input bits -Activate Enable inputs Example : G2A Y0 Y1 Y2 Y3 A B Z Y 74x138 Y4 Y5 Y6 Y7 CX G2B G1 F +5V

15 Decoder cascading 4-to-16 decoder

16 Decoder applications Microprocessor memory systems  selecting different banks of memory Microprocessor input/output systems  selecting different devices Microprocessor instruction decoding  enabling different functional units Memory chips  enabling different rows of memory depending on address Lots of other applications

17 Next… Encoders Reading Wakerly CH-6.5