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Encoder & Decoder

S
Syed Saeed

This document discusses decoders and encoders. It defines a decoder as a circuit that accepts a binary input and activates only one output corresponding to the input. An encoder is the inverse, converting an active input to a coded output. Various types of decoders and encoders are described, including 2-to-4 decoders, 3-to-8 decoders, priority encoders, decimal-to-BCD encoders, and octal-to-binary encoders. Truth tables and logic diagrams are provided as examples. Expansion of decoders using multiple lower-order decoders is also covered.

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SYED HASAN SAEED hasansaeedcontrol@gmail.com https://shasansaeed.yolasite.com 1 Syed Hasan Saeed, Integral University, Lucknow
DECODER & ENCODER Syed Hasan Saeed, Integral University, Lucknow 2
DECODER • A decoder is a combinational circuit. • A decoder accepts a set of inputs that represents a binary number and activates only that output corresponding to the input number. All other outputs remain inactive. • Fig. 1 shows the block diagram of decoder with ‘N’ inputs and ‘M’ outputs. • There are 2N possible input combinations, for each of these input combination only one output will be HIGH (active) all other outputs are LOW • Some decoder have one or more ENABLE (E) inputs that are used to control the operation of decoder. Syed Hasan Saeed, Integral University, Lucknow 3
BLOCK DIAGRAM OF DECODER Syed Hasan Saeed, Integral University, Lucknow 4 DECODER A0 A1 A2 AN-1 . . . . N- Inputs M- Outputs . . . . B0 B1 B2 BM-1 Only one output is High for each input Fig. 1
2 to 4 Line Decoder:  Block diagram of 2 to 4 decoder is shown in fig. 2  A and B are the inputs. ( No. of inputs =2)  No. of possible input combinations: 22=4  No. of Outputs : 22=4, they are indicated by D0, D1, D2 and D3  From the Truth Table it is clear that each output is “1” for only specific combination of inputs. Syed Hasan Saeed, Integral University, Lucknow 5 A B D0 D1 D2 D3 2 X 4 Decoder INPUTS OUTPUTS A B D0 D1 D2 D3 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 Fig. 2 TRUTH TABLE Inputs Outputs
BOOLEAN EXPRESSION: Syed Hasan Saeed, Integral University, Lucknow 6 ABDBAD BADBAD 32 10   From Truth Table LOGIC DIAGRAM: A A B B BAD0  BAD1  BAD2  BAD3  Fig. 3
3 to 8 Line Decoder:  Block diagram of 3 to 8 decoder is shown in fig. 4  A , B and C are the inputs. ( No. of inputs =3)  No. of possible input combinations: 23=8  No. of Outputs : 23=8, they are indicated by D0 to D7  From the Truth Table it is clear that each output is “1” for only specific combination of inputs. Syed Hasan Saeed, Integral University, Lucknow 7 A B D0 D7 3 X 8 Decoder C . . . . Fig. 4 Inputs Outputs
TRUTH TABLE FOR 3 X 8 DECODER: Syed Hasan Saeed, Integral University, Lucknow 8 INPUTS OUTPUTS A B C D0 D1 D2 D3 D4 D5 D6 D7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 CBAD0  CBAD1  CBAD2  CBAD3  CBAD4  CBAD5  CBAD6  CBAD7 
LOGIC DIAGRAM OF 3 X 8 DECODER: Syed Hasan Saeed, Integral University, Lucknow 9 CBAD0  CBAD1  CBAD2  CBAD3  CBAD4  CBAD5  CBAD6  CBAD7  A B C A B C OUTPUTS INPUTS Fig. 5
EXPANSION OF DECODERS: The number of lower order Decoder for implementing higher order Decoder can be find as No. of lower order required = m2/m1 Where, m1=No. of Outputs of lower order Decoder m2=No. of Outputs of higher order Decoder Syed Hasan Saeed, Integral University, Lucknow 10
3 x 8 Decoder From 2 x 4 Decoder: Syed Hasan Saeed, Integral University, Lucknow 11 2 x 4 Decoder 2 x 4 Decoder X Y E D0 D1 D2 D3 D4 D5 D6 D7 OUTPUT INPUT Fig. 6
Example: Implement the following multiple output function using a suitable Decoder. f1(A, B, C) = ∑m(0,4,7)+ d(2,3) f2 (A, B, C) =∑m (1,5,6) f3 (A, B, C) =∑m (0,2,4,6) Solution: f1 consists of don’t care conditions. So we consider them to be logic 1. Syed Hasan Saeed, Integral University, Lucknow 12 0 1 2 3 4 5 6 7 f1(A, B, C) f2 (A, B, C) f3 (A, B, C) 3x8Decoder A B C INPUTS Fig. 7
EXAMPLE: Implement the following Boolean function using suitable Decoder. f1 (x,y,z)=∑m(1,5,7) f2 (x,y,z)=∑m(0,3) f3 (x,y,z)=∑m(2,4,5) Solution: Syed Hasan Saeed, Integral University, Lucknow 13 X Y Z E 3X8Decoder 0 1 2 3 4 5 6 7 INPUTS f1 (x,y,z) f2 (x,y,z) f3 (x,y,z) Fig. 8
EXAMPLE: A combinational circuit is defined by the following Boolean function. Design circuit with a Decoder and external gate. Syed Hasan Saeed, Integral University, Lucknow 14 zxzyxz)y,x,(F zxzyxz)y,(x,F 2 1   SOLUTION: STEP 1: Write the given function F1 in SOP form (1,3,6)mz)y,x,(F zyxzyxzyxz)y,x,(F zx)yy(zyxz)y,x,(F zxzyxz)y,x,(F (0,5,7)mz)y,x,(F zyxzyxzyxz)y,x,(F zx)yy(zyxz)y,x,(F 2 2 2 2 1 1 1        (UPTU, 2004-05)
Boolean Function using Decoder: Syed Hasan Saeed, Integral University, Lucknow 15 0 1 2 3 4 5 6 7 F1 F2 3 x 8 Decoder X Y Z Fig. 9
ENCODER • An Encoder is a combinational logic circuit. • It performs the inverse operation of Decoder. • The opposite process of decoding is known as Encoding. • An Encoder converts an active input signal into a coded output signal. • Block diagram of Encoder is shown in Fig.10. It has ‘M’ inputs and ‘N’ outputs. • An Encoder has ‘M’ input lines, only one of which is activated at a given time, and produces an N-bit output code, depending on which input is activated. Syed Hasan Saeed, Integral University, Lucknow 16 ------- ------- ‘M’Inputs ‘N’Outputs Encoder A0 A1 A2 AM-1 B0 B1 B2 BN-1 Fig. 10
• Encoders are used to translate the rotary or linear motion into a digital signal. • The difference between Decoder and Encoder is that Decoder has Binary Code as an input while Encoder has Binary Code as an output. • Encoder is an Electronics device that converts the analog signal to digital signal such as BCD Code. • Types of Encoders i. Priority Encoder ii. Decimal to BCD Encoder iii. Octal to Binary Encoder iv. Hexadecimal to Binary Encoder Syed Hasan Saeed, Integral University, Lucknow 17
ENCODER Syed Hasan Saeed, Integral University, Lucknow 18 Encoder 4 x 2 A0 A1 A2 Fig. 11 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output B0 B1 B2 B3
ENCODER Syed Hasan Saeed, Integral University, Lucknow 19 Encoder 4 x 2 A0 A1 A2 Fig. 12 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output 00 01 10 11
ENCODER Syed Hasan Saeed, Integral University, Lucknow 20 Encoder 4 x 2 A0 A1 A2 Fig. 13 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output 00 01 10 11 1 0
ENCODER Syed Hasan Saeed, Integral University, Lucknow 21 Encoder 4 x 2 A0 A1 A2 Fig. 14 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output 00 01 10 11 1 0 10
PRIORITY ENCODER: • As the name indicates, the priority is given to inputs line. • If two or more input lines are high at the same time i.e 1 at the same time, then the input line with high priority shall be considered. • Block diagram and Truth table of Priority Encoder are shown in fig.15 Syed Hasan Saeed, Integral University, Lucknow 22 D3 D2 D1 D0 Y1 Y0 Highest Priority Input Lowest Priority Input Output Priority Encoder INPUTS OUTPUTS V 0 0 0 0 x x 0 0 0 0 1 0 0 1 0 0 1 x 0 1 1 0 1 x x 1 0 1 1 x x x 1 1 1 D3 D2 D1 D0 Y1 Y0 TRUTH TABLE: Fig.15Block Diagram of Priority Encoder
• There are four inputs D0, D1,D2, D3 and two outputs Y1 and Y2. • D3 has highest priority and D0 is at lowest priority. • If D3=1 irrespective of other inputs then output Y1Y0=11. • D3 is at highest priority so other inputs are considered as don’t care. Syed Hasan Saeed, Integral University, Lucknow 23 X 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 D3D2 D3D2 D1D0 D1D0 00 01 11 10 00 01 11 10 00 01 11 10 10 11 01 00 1230 DDDY 321 DDY  K-map for Y1 and Y0 Fig. 16
LOGIC DIAGRAM OF PRIORITY ENCODER: Syed Hasan Saeed, Integral University, Lucknow 24 321 DDY  1230 DDDY  D3 D2 D1 D0 Y1 Y0 Fig. 17
DECIMAL TO BCD ENCODER: • It has ten inputs corresponding to ten decimal digits (from 0 to 9) and four outputs (A,B,C,D) representing the BCD. • The block diagram is shown in fig.18 and Truth table in fig.19 Syed Hasan Saeed, Integral University, Lucknow 25 --------- ENCODER 0 1 2 9 A B C D INPUTS OUTPUTS Fig. 18
Truth table: Syed Hasan Saeed, Integral University, Lucknow 26 INPUTS BCD OUTPUTS 0 1 2 3 4 5 6 7 8 9 A B C D 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 Fig. 19
• From Truth Table it is clear that the output A is HIGH when input is 8 OR 9 is HIGH Therefore A=8+9 • The output B is HIGH when 4 OR 5 OR 6 OR 7 is HIGH Therefore B=4+5+6+7 • The output C is HIGH when 2 OR 3 OR 6 OR 7 is HIGH Therefore C=2+3+6+7 • Similarly D=1+3+5+7+9 Logic Diagram is shown in fig.20 Syed Hasan Saeed, Integral University, Lucknow 27
DECIMAL TO BCD ENCODER Syed Hasan Saeed, Integral University, Lucknow 28 0 1 2 3 4 5 6 7 8 9 A B C D +5V Fig. 20
OCTAL TO BINARY ENCODER: • Block Diagram of Octal to Binary Encoder is shown in Fig. 21 • It has eight inputs and three outputs. • Only one input has one value at any given time. • Each input corresponds to each octal digit and output generates corresponding Binary Code. Syed Hasan Saeed, Integral University, Lucknow 29 D0 D1 D2 D3 D4 D5 D6 D7 X Y Z INPUT OUTPUT ENCODER Fig. 21
TRUTH TABLE: Syed Hasan Saeed, Integral University, Lucknow 30 INPUT OUTPUT D0 D1 D2 D3 D4 D5 D6 D7 X Y Z 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 Fig.22
From Truth table: • It is assume that only one input is HIGH at any given time. If two outputs are HIGH then undefined output will produced. For example D3 and D6 are HIGH, then output of Encoder will be 111. This output neither equivalent code corresponding to D3 nor to D6. • To overcome this problem, priorities should be assigned to each input. • Form the truth table it is clear that the output X becomes 1 if any of the digit D4 or D5 or D6 or D7 is 1. • D0 is considered as don’t care because it is not shown in expression. • If inputs are zero then output will be zero. Similarly if D0 is one, the output will be zero. • Syed Hasan Saeed, Integral University, Lucknow 31 7531 7632 7654 DDDD DDDDY DDDDX    Z
Syed Hasan Saeed, Integral University, Lucknow 32 7531 7632 7654 DDDD DDDDY DDDDX    Z D0 D2 D3 D4 D5 D6 D7 D1 7654 DDDDX  7632 DDDDY  7531 DDDD Z Fig. 23 LOGIC DIAGRAM:
THANK YOU Syed Hasan Saeed, Integral University, Lucknow 33
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Encoder & Decoder

  • 2. DECODER & ENCODER Syed Hasan Saeed, Integral University, Lucknow 2
  • 3. DECODER • A decoder is a combinational circuit. • A decoder accepts a set of inputs that represents a binary number and activates only that output corresponding to the input number. All other outputs remain inactive. • Fig. 1 shows the block diagram of decoder with ‘N’ inputs and ‘M’ outputs. • There are 2N possible input combinations, for each of these input combination only one output will be HIGH (active) all other outputs are LOW • Some decoder have one or more ENABLE (E) inputs that are used to control the operation of decoder. Syed Hasan Saeed, Integral University, Lucknow 3
  • 4. BLOCK DIAGRAM OF DECODER Syed Hasan Saeed, Integral University, Lucknow 4 DECODER A0 A1 A2 AN-1 . . . . N- Inputs M- Outputs . . . . B0 B1 B2 BM-1 Only one output is High for each input Fig. 1
  • 5. 2 to 4 Line Decoder:  Block diagram of 2 to 4 decoder is shown in fig. 2  A and B are the inputs. ( No. of inputs =2)  No. of possible input combinations: 22=4  No. of Outputs : 22=4, they are indicated by D0, D1, D2 and D3  From the Truth Table it is clear that each output is “1” for only specific combination of inputs. Syed Hasan Saeed, Integral University, Lucknow 5 A B D0 D1 D2 D3 2 X 4 Decoder INPUTS OUTPUTS A B D0 D1 D2 D3 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 Fig. 2 TRUTH TABLE Inputs Outputs
  • 6. BOOLEAN EXPRESSION: Syed Hasan Saeed, Integral University, Lucknow 6 ABDBAD BADBAD 32 10   From Truth Table LOGIC DIAGRAM: A A B B BAD0  BAD1  BAD2  BAD3  Fig. 3
  • 7. 3 to 8 Line Decoder:  Block diagram of 3 to 8 decoder is shown in fig. 4  A , B and C are the inputs. ( No. of inputs =3)  No. of possible input combinations: 23=8  No. of Outputs : 23=8, they are indicated by D0 to D7  From the Truth Table it is clear that each output is “1” for only specific combination of inputs. Syed Hasan Saeed, Integral University, Lucknow 7 A B D0 D7 3 X 8 Decoder C . . . . Fig. 4 Inputs Outputs
  • 8. TRUTH TABLE FOR 3 X 8 DECODER: Syed Hasan Saeed, Integral University, Lucknow 8 INPUTS OUTPUTS A B C D0 D1 D2 D3 D4 D5 D6 D7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 CBAD0  CBAD1  CBAD2  CBAD3  CBAD4  CBAD5  CBAD6  CBAD7 
  • 9. LOGIC DIAGRAM OF 3 X 8 DECODER: Syed Hasan Saeed, Integral University, Lucknow 9 CBAD0  CBAD1  CBAD2  CBAD3  CBAD4  CBAD5  CBAD6  CBAD7  A B C A B C OUTPUTS INPUTS Fig. 5
  • 10. EXPANSION OF DECODERS: The number of lower order Decoder for implementing higher order Decoder can be find as No. of lower order required = m2/m1 Where, m1=No. of Outputs of lower order Decoder m2=No. of Outputs of higher order Decoder Syed Hasan Saeed, Integral University, Lucknow 10
  • 11. 3 x 8 Decoder From 2 x 4 Decoder: Syed Hasan Saeed, Integral University, Lucknow 11 2 x 4 Decoder 2 x 4 Decoder X Y E D0 D1 D2 D3 D4 D5 D6 D7 OUTPUT INPUT Fig. 6
  • 12. Example: Implement the following multiple output function using a suitable Decoder. f1(A, B, C) = ∑m(0,4,7)+ d(2,3) f2 (A, B, C) =∑m (1,5,6) f3 (A, B, C) =∑m (0,2,4,6) Solution: f1 consists of don’t care conditions. So we consider them to be logic 1. Syed Hasan Saeed, Integral University, Lucknow 12 0 1 2 3 4 5 6 7 f1(A, B, C) f2 (A, B, C) f3 (A, B, C) 3x8Decoder A B C INPUTS Fig. 7
  • 13. EXAMPLE: Implement the following Boolean function using suitable Decoder. f1 (x,y,z)=∑m(1,5,7) f2 (x,y,z)=∑m(0,3) f3 (x,y,z)=∑m(2,4,5) Solution: Syed Hasan Saeed, Integral University, Lucknow 13 X Y Z E 3X8Decoder 0 1 2 3 4 5 6 7 INPUTS f1 (x,y,z) f2 (x,y,z) f3 (x,y,z) Fig. 8
  • 14. EXAMPLE: A combinational circuit is defined by the following Boolean function. Design circuit with a Decoder and external gate. Syed Hasan Saeed, Integral University, Lucknow 14 zxzyxz)y,x,(F zxzyxz)y,(x,F 2 1   SOLUTION: STEP 1: Write the given function F1 in SOP form (1,3,6)mz)y,x,(F zyxzyxzyxz)y,x,(F zx)yy(zyxz)y,x,(F zxzyxz)y,x,(F (0,5,7)mz)y,x,(F zyxzyxzyxz)y,x,(F zx)yy(zyxz)y,x,(F 2 2 2 2 1 1 1        (UPTU, 2004-05)
  • 15. Boolean Function using Decoder: Syed Hasan Saeed, Integral University, Lucknow 15 0 1 2 3 4 5 6 7 F1 F2 3 x 8 Decoder X Y Z Fig. 9
  • 16. ENCODER • An Encoder is a combinational logic circuit. • It performs the inverse operation of Decoder. • The opposite process of decoding is known as Encoding. • An Encoder converts an active input signal into a coded output signal. • Block diagram of Encoder is shown in Fig.10. It has ‘M’ inputs and ‘N’ outputs. • An Encoder has ‘M’ input lines, only one of which is activated at a given time, and produces an N-bit output code, depending on which input is activated. Syed Hasan Saeed, Integral University, Lucknow 16 ------- ------- ‘M’Inputs ‘N’Outputs Encoder A0 A1 A2 AM-1 B0 B1 B2 BN-1 Fig. 10
  • 17. • Encoders are used to translate the rotary or linear motion into a digital signal. • The difference between Decoder and Encoder is that Decoder has Binary Code as an input while Encoder has Binary Code as an output. • Encoder is an Electronics device that converts the analog signal to digital signal such as BCD Code. • Types of Encoders i. Priority Encoder ii. Decimal to BCD Encoder iii. Octal to Binary Encoder iv. Hexadecimal to Binary Encoder Syed Hasan Saeed, Integral University, Lucknow 17
  • 18. ENCODER Syed Hasan Saeed, Integral University, Lucknow 18 Encoder 4 x 2 A0 A1 A2 Fig. 11 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output B0 B1 B2 B3
  • 19. ENCODER Syed Hasan Saeed, Integral University, Lucknow 19 Encoder 4 x 2 A0 A1 A2 Fig. 12 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output 00 01 10 11
  • 20. ENCODER Syed Hasan Saeed, Integral University, Lucknow 20 Encoder 4 x 2 A0 A1 A2 Fig. 13 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output 00 01 10 11 1 0
  • 21. ENCODER Syed Hasan Saeed, Integral University, Lucknow 21 Encoder 4 x 2 A0 A1 A2 Fig. 14 Decoder 2 x 4A3 M=4 M=22 M=2N ‘M’ is the input and ‘N’ is the output 00 01 10 11 1 0 10
  • 22. PRIORITY ENCODER: • As the name indicates, the priority is given to inputs line. • If two or more input lines are high at the same time i.e 1 at the same time, then the input line with high priority shall be considered. • Block diagram and Truth table of Priority Encoder are shown in fig.15 Syed Hasan Saeed, Integral University, Lucknow 22 D3 D2 D1 D0 Y1 Y0 Highest Priority Input Lowest Priority Input Output Priority Encoder INPUTS OUTPUTS V 0 0 0 0 x x 0 0 0 0 1 0 0 1 0 0 1 x 0 1 1 0 1 x x 1 0 1 1 x x x 1 1 1 D3 D2 D1 D0 Y1 Y0 TRUTH TABLE: Fig.15Block Diagram of Priority Encoder
  • 23. • There are four inputs D0, D1,D2, D3 and two outputs Y1 and Y2. • D3 has highest priority and D0 is at lowest priority. • If D3=1 irrespective of other inputs then output Y1Y0=11. • D3 is at highest priority so other inputs are considered as don’t care. Syed Hasan Saeed, Integral University, Lucknow 23 X 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 D3D2 D3D2 D1D0 D1D0 00 01 11 10 00 01 11 10 00 01 11 10 10 11 01 00 1230 DDDY 321 DDY  K-map for Y1 and Y0 Fig. 16
  • 24. LOGIC DIAGRAM OF PRIORITY ENCODER: Syed Hasan Saeed, Integral University, Lucknow 24 321 DDY  1230 DDDY  D3 D2 D1 D0 Y1 Y0 Fig. 17
  • 25. DECIMAL TO BCD ENCODER: • It has ten inputs corresponding to ten decimal digits (from 0 to 9) and four outputs (A,B,C,D) representing the BCD. • The block diagram is shown in fig.18 and Truth table in fig.19 Syed Hasan Saeed, Integral University, Lucknow 25 --------- ENCODER 0 1 2 9 A B C D INPUTS OUTPUTS Fig. 18
  • 26. Truth table: Syed Hasan Saeed, Integral University, Lucknow 26 INPUTS BCD OUTPUTS 0 1 2 3 4 5 6 7 8 9 A B C D 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 Fig. 19
  • 27. • From Truth Table it is clear that the output A is HIGH when input is 8 OR 9 is HIGH Therefore A=8+9 • The output B is HIGH when 4 OR 5 OR 6 OR 7 is HIGH Therefore B=4+5+6+7 • The output C is HIGH when 2 OR 3 OR 6 OR 7 is HIGH Therefore C=2+3+6+7 • Similarly D=1+3+5+7+9 Logic Diagram is shown in fig.20 Syed Hasan Saeed, Integral University, Lucknow 27
  • 28. DECIMAL TO BCD ENCODER Syed Hasan Saeed, Integral University, Lucknow 28 0 1 2 3 4 5 6 7 8 9 A B C D +5V Fig. 20
  • 29. OCTAL TO BINARY ENCODER: • Block Diagram of Octal to Binary Encoder is shown in Fig. 21 • It has eight inputs and three outputs. • Only one input has one value at any given time. • Each input corresponds to each octal digit and output generates corresponding Binary Code. Syed Hasan Saeed, Integral University, Lucknow 29 D0 D1 D2 D3 D4 D5 D6 D7 X Y Z INPUT OUTPUT ENCODER Fig. 21
  • 30. TRUTH TABLE: Syed Hasan Saeed, Integral University, Lucknow 30 INPUT OUTPUT D0 D1 D2 D3 D4 D5 D6 D7 X Y Z 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 Fig.22
  • 31. From Truth table: • It is assume that only one input is HIGH at any given time. If two outputs are HIGH then undefined output will produced. For example D3 and D6 are HIGH, then output of Encoder will be 111. This output neither equivalent code corresponding to D3 nor to D6. • To overcome this problem, priorities should be assigned to each input. • Form the truth table it is clear that the output X becomes 1 if any of the digit D4 or D5 or D6 or D7 is 1. • D0 is considered as don’t care because it is not shown in expression. • If inputs are zero then output will be zero. Similarly if D0 is one, the output will be zero. • Syed Hasan Saeed, Integral University, Lucknow 31 7531 7632 7654 DDDD DDDDY DDDDX    Z
  • 32. Syed Hasan Saeed, Integral University, Lucknow 32 7531 7632 7654 DDDD DDDDY DDDDX    Z D0 D2 D3 D4 D5 D6 D7 D1 7654 DDDDX  7632 DDDDY  7531 DDDD Z Fig. 23 LOGIC DIAGRAM:
  • 33. THANK YOU Syed Hasan Saeed, Integral University, Lucknow 33