Company LOGO DKT 1223 DIGITAL SYSTEM 1 E

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 WEEK #8 FUNCTIONS OF COMBINATIONAL LOGIC (ENCODER & DECODER, MUX & DEMUX)

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

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

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

Encoder 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 Company LOGO Draw a Truth-Table showing input and output DECIMAL DIGIT BCD CODE A 3 A 2 A 1 A 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 5 0 1 6 0 1 1 0 7 0 1 1 1 8 1 0 0 0 9 1 0 0 1

Encoder Company LOGO (a) (b) From the Truth-Table, get the equation for each output: A 3= A 2= A 1= A 0= Σ Σ m(8, m(4, m(2, m(1, 9) 5, 6, 7) 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 (b)

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

Decoder Company LOGO Basic Binary Decoder Example: Ü To determine when a binary 1001 occurs on the input of a digital circuit, AND gate can be used as the basic decoding element. Ü AND gate -> produce HIGH output when all inputs are HIGH Ü 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 Company LOGO Question 2: (a) Determine the logic required to decode the binary 11100 by producing a high level (active-HIGH) on the output. A 4 A 3 A 2 Active-HIGH produce HIGH output A 1 Decoding function, A 0

Decoder Company LOGO 4 -bit Decoder Ü This type of decoder is called 4 -line-to-16 -line decoder or 1 -of-16 decoder Ü For a 4 -bit decoder, there are 16 possible combinations (24=16). This means that 16 decoding gates are required

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

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

Multiplexers (MUX) Company LOGO Ü MUX is a device that allows digital information from several sources to be routed onto a single line for transmission Ü 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. Ü MUX is also known as data selectors n select inputs 1 data output 2 n data inputs Logic symbol for a 4 -input multiplexer (4: 1 MUX)

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

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

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

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

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

Demultiplexers (DEMUX) Company LOGO 1: 4 DEMUX

Demultiplexers (DEMUX) Company LOGO Question 4: Construct a 1: 4 DEMUX using block diagram. Show the equivalent Truth-Table. I 0 1 -4 DEMUX Q 0 Q 1 Q 2 Q 3 S 1 S 0 Block diagram S 1 S 0 I 0 Q 1 Q 2 Q 3 Logic circuit Truth-table S 1 S 0 I 1 Q 3 Q 2 Q 1 Q 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 E D N