DKT 122/3 DIGITAL SYSTEM 1

Transcription

1 Company LOGO DKT 122/3 DIGITAL SYSTEM 1 E d i t y o u r s l o g a n h e r e CHAPTER 6 FUNCTIONS OF COMBINATIONAL LOGIC (ENCODER & DECODER, MUX & DEMUX)

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

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

4 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 Encoder 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

6 Encoder Draw a Truth-Table showing input and output DECIMAL BCD CODE DIGIT A 3 A 2 A 1 A

7 Encoder (b) From the Truth-Table, get the equation for each output: A 3 = I 8 OR I 9 A 2 = I 4 OR I 5 OR I 6 OR I 7 A 1 = I 2 OR I 3 OR I 6 OR I 7 A 0 = I 1 OR I 3 OR I 5 OR I 7 OR I 9 (c) Based on the output equation, draw a circuit for basic decimal-to-bcd encoder (a) (b) (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

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

9 Decoder 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 Decoding logic for the binary code 1001 with an active-high output.

10 Decoder Question 2: (a) Determine the logic required to decode the binary by producing a high level (active-high) on the output. A 4 A 3 A 2 A 1 A 0 Active-HIGH produce HIGH output Decoding function, Decodingfu nction, X A A A A A

11 Decoder 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

12 Decoder 3 to 8 Binary Decoder Question: Is this active-high or active-low output?

13 -- don t care inputs -- Company LOGO Decoder 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 nondecimal 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

14 Multiplexers (MUX) Company LOGO 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 datainput 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 n select inputs 2 n data inputs 1 data output Logic symbol for a 4-input multiplexer (4:1 MUX)

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

16 Multiplexers (MUX) 4:1 MUX 2 data-select lines means that any one of the 4 data-input lines can be selected DATA-SELECT INPUTS S 0 S 1 INPUT SELECTED D 0 D 1 D 2 D 0 D 1 D 2 4-to-1 MUX Z Z 0 0 D D D 2 D 3 D 3 S 1 S D 3 S 1 S 0 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

17 4:1 MUX Multiplexers (MUX) Logic diagram for 4:1 MUX Total expression for the data output is: Y D 0 S1S0 D1 S1S0 D2S1 S0 D3S1S 0

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

19 Demultiplexers (DEMUX) Company LOGO 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 data input n select inputs 2 n data outputs 1-line to 4-line DEMUX

20 Demultiplexers (DEMUX) 1:4 DEMUX

21 Demultiplexers (DEMUX) Question 4: Construct a 1:4 DEMUX using block diagram. Show the equivalent Truth-Table. Q Q I 1 0 DEMUX Q 2 Truth-table S1 S0 I1 Q3 Q2 Q1 Q0 S 1 S 0 I 0 S 1 S 0 Q 3 Block diagram Q0 Q1 Q Q3 Logic circuit