1. Company LOGO Edit your slogan here DKT 122/3 DIGITAL SYSTEM 1 WEEK #8 FUNCTIONS OF COMBINATIONAL LOGIC (ENCODER & DECODER, MUX & DEMUX)

2. Company LOGO Topic Outlines  Encoder  Decoder  Multiplexers (MUX)  Demultiplexers (DEMUX)

3. Company LOGO Topic Outlines  Encoder  Decoder  Multiplexers (MUX) Multiplexers (MUX)  Demultiplexers (DEMUX)

4. Company LOGO Encoder  Encoder converts information such as decimal number, alphabetical character, or symbols into some coded form, such as BCD or binary  Encoder is usually used for:  Data representation  Data security

5. Company LOGO Question 1: Design a Decimal to BCD Encoder Hints: (a)Draw a Truth-Table showing input and output - How many inputs? : 10 (0 to 9) - How many outputs? : 4 because we need 4 bits to express 9 (1001) (b) From the Truth-Table, get the equation for each output - How many Boolean expression? : 4 since there are 4 outputs (c) Based on the output equation, draw a circuit for basic decimal-to-BCD encoder Encoder

6. Company LOGO Draw a Truth-Table showing input and output DECIMAL DIGIT BCD CODE A3A3 A2A2 A1A1 A0A0 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001 Encoder

7. Company LOGO (b) From the Truth-Table, get the equation for each output: A 3 = Σ m(8, 9) A 2 = Σ m(4, 5, 6, 7) A 1 = Σ m(2, 3, 6, 7) A 0 = Σ m(1, 3, 5, 7, 9) (c) Based on the output equation, draw a circuit for basic decimal-to-BCD encoder (a) Logic symbol for a 10-line-to 4 line encoder (b) Logic diagram. A 0-digit input is not needed because the BCD outputs are all low when there are no HIGH inputs (a) (b) Encoder

8. Company LOGO  A decoder is a circuit that creates an output based on the binary states of a given input  Do the opposite of encoder Decoder Decoder block diagram

9. Company LOGO Basic Binary Decoder Example:  To determine when a binary 1001 occurs on the input of a digital circuit, AND gate can be used as the basic decoding element.  AND gate -> produce HIGH output when all inputs are HIGH  How to ensure that inputs to the AND gate are HIGH when binary 1001 occurs? Other than this input combinations, the output is 0 Decoder

10. Company LOGO Question 2: (a)Determine the logic required to decode the binary 11100 by producing a high level (active-HIGH) on the output. Active-HIGH  produce HIGH output Decoding function, A4A4 A2A2 A1A1 A0A0 A3A3 Decoder

11. Company LOGO 4-bit Decoder  This type of decoder is called 4-line-to-16-line decoder or 1-of-16 decoder  For a 4-bit decoder, there are 16 possible combinations (2 4 =16). This means that 16 decoding gates are required Decoder

12. Company LOGO 3 to 8 Binary Decoder Question : Is this active-HIGH or active-LOW output? Decoder

13. Company LOGO Example: Seven Segment Decoder A seven segment decoder has 4-bit BCD input and the seven segment display code as its output: In minimizing the circuits for the segment outputs all non- decimal input combinations (1010, 1011, 1100,1101, 1110, 1111) are taken as don’t-cares D C B A a b c d e f g 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 -- don’t care inputs -- Decoder

14. Company LOGO Multiplexers (MUX)  MUX is a device that allows digital information from several sources to be routed onto a single line for transmission  It is made up of several data- input lines and a single output line. It also has data-select inputs which permits digital data on any one of the inputs to be switched to the output line.  MUX is also known as data selectors Logic symbol for a 4-input multiplexer (4:1 MUX) n select inputs 1 data output 2 n data inputs

15. Company LOGO 2:1 MUX Logic circuit Truth-table Multiplexers (MUX)

16. Company LOGO DATA-SELECT INPUTS INPUT SELECTED S0S0 S1S1 00D0D0 01D1D1 10D2D2 11D3D3 If a binary 0 (S 0 =0 and S 1 =0) is applied to the data-select lines, the data on input D 0 appear on the data-output line 2 data-select lines means that any one of the 4 data-input lines can be selected 4-to-1 MUX S0S0 Z D1D1 D0D0 S1S1 D3D3 D2D2 D0D0 D1D1 D2D2 D3D3 S1S1 S0S0 Z 4:1 MUX Multiplexers (MUX)

17. Company LOGO Total expression for the data output is: Logic diagram for 4:1 MUX 4:1 MUX Multiplexers (MUX)

18. Company LOGO Question 3: Construct an 8:1 multiplexer using block diagram. 8 input lines means there must be 3 data select lines. Multiplexers (MUX)

19. Company LOGO Demultiplexers (DEMUX)  DEMUX reverse the multiplexing functions  It takes digital information from one line and distributes it to a given number of output lines  DEMUX is also known as data distributor 1-line to 4-line DEMUX 1 data input n select inputs 2 n data outputs

20. Company LOGO 1:4 DEMUX Demultiplexers (DEMUX)

21. Company LOGO Question 4: Construct a 1:4 DEMUX using block diagram. Show the equivalent Truth-Table. 1-4 DEMUX S 0 I 0 Q 1 Q 0 S 1 Q 3 Q 2 1-4 S 0 I 0 Q 1 Q 0 S 1 Q 3 Q 2 S0S0 S1S1 Q0 Q1 I 0 Q2 Q3 S1S0I1Q3Q2Q1Q0 0010001 0110010 1010100 1111000 Truth-table Block diagram Logic circuit Demultiplexers (DEMUX) END