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Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS
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Transcript of Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS
![Page 1: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/1.jpg)
Chapter 11Chapter 11
CODES, CONVERTERS, COMPARATORS, AND LOGIC
OPERATION PROCESSING CIRCUITS
![Page 2: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/2.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Lesson 1
Decimal Number Codes
![Page 3: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/3.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Outline• BCD (8421) code• Excess 3-Code BCD Code• 7536 code• 2421 code• 5421 code
![Page 4: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/4.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
yypmax pmax ––1 1 ×××××××× ww00pmax pmax ––1 1 + y+ ypmax pmax ––22 ××××××××
ww00pmax pmax ––2 2 ×××××××× yypmax pmax ––33 x wx w00
pmax pmax ––3 3
++………………. + . + yy22 ×××××××× ww002 2 + y+ y11 ×××××××× ww00
1 1
++ yy00 ×××××××× ww0000 , , …………………………. (1). (1)
General Formula N = sum of the yp (Base)p
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Place value and base (weight)Place value and base (weight)
�� p = place of the digit = 0, 1, 2, p = place of the digit = 0, 1, 2, ……., (pmax ., (pmax –– 3), (pmax 3), (pmax –– 2) or (pmax 2) or (pmax –– 1), from right 1), from right to leftto left
�� pmax = maximum the number of places pmax = maximum the number of places used in the representation andused in the representation and
�� w0 = base (basic weight)w0 = base (basic weight)
�� y = 0 or 1 in binary formy = 0 or 1 in binary form
![Page 6: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/6.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
8421 code Place value and base 8421 code Place value and base (weight)(weight)
�� At place = 3, weight is 8At place = 3, weight is 8
�� At place = 2, weight is 4At place = 2, weight is 4
�� At place = 1, weight is 2At place = 1, weight is 2
�� At place = 0, weight is 4At place = 0, weight is 4
�� At each place weight = wAt each place weight = w0pp
�� w0 = base (basic weight) = 2w0 = base (basic weight) = 2
![Page 7: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/7.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
8421 code Place value and base 8421 code Place value and base (weight)(weight)
�� At place = 4, weight is 10At place = 4, weight is 10
�� At place = 5, weight is 20At place = 5, weight is 20
�� At place = 6, weight is 40At place = 6, weight is 40
�� At place = 7, weight is 80At place = 7, weight is 80
�� w0 = base (basic weight) = 2w0 = base (basic weight) = 2
![Page 8: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/8.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Outline• BCD Code• Excess 3-Code BCD Code• 7536 code• 2421 code• 5421 code
![Page 9: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/9.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Excess 3-Code (XS-3) BCD Code
• Start not from 0 but from 0011• Formula is N = 3 + yypmax pmax ––1 1 ×××××××× ww00
pmax pmax ––1 1 + + yypmax pmax ––22 ×××××××× ww00
pmax pmax ––2 2 ×××××××× yypmax pmax ––33 x wx w00pmax pmax
––3 3 ++………………. + . + yy22 ×××××××× ww002 2 + y+ y11 ×××××××× ww00
1 1 ++yy00 ×××××××× ww00
00 , , …………………………. (2). (2)•• y = 0 or 1 in binary formy = 0 or 1 in binary form
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
XSXS--3 code Place value and base 3 code Place value and base (weight)(weight)
�� At place = 3, weight is 8At place = 3, weight is 8
�� At place = 2, weight is 4At place = 2, weight is 4
�� At place = 1, weight is 2At place = 1, weight is 2
�� At place = 0, weight is 4At place = 0, weight is 4
�� At each place weight = wAt each place weight = w0pp
�� w0 = base (basic weight) = 2w0 = base (basic weight) = 2
![Page 11: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/11.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
XSXS--3 code Place value and base 3 code Place value and base (weight)(weight)
�� At place = 4, weight is 10At place = 4, weight is 10
�� At place = 5, weight is 20At place = 5, weight is 20
�� At place = 6, weight is 40At place = 6, weight is 40
�� At place = 7, weight is 80At place = 7, weight is 80
�� At each place weight = wAt each place weight = w0pp
�� w0 = base (basic weight) = 2w0 = base (basic weight) = 2
![Page 12: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/12.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Start from 0011• XS-3 codes are 0011bxs3, 0100bxs3, 0101bxs3,
0110bxs3, 0111bxs3, 1000bxs3, 1001bxs3, 1010bxs3, 1011bxs3 and 1100b for 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 for ten decimal numbers, respectively.
• A feature of this code is that for each decimal number is self-complementing. Complement of 0 is 9. Similarly XS-3 code for 0 is 0011 and for 9 it is 1100. Complement of 1 is 8. Similarly XS-3 code for 0 is 0100 and for 8 it is 1011
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Excess 3 code conversion by 4-bit Adder for A3A2A1A0 BCD number
F.A F.AF.AF.A
S3 S2 S1 S0
Cy3 Cy2 Cy1 Cy0 Cy-1
0
A3 0 A2 0 A1 1 A0 1
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Outline• BCD Code• Excess 3-Code BCD Code• 7536 code• 2421 code• 5421 code
![Page 15: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/15.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
7536 Code
• Formula is N = yy7 7 ×××××××× ww77 + y+ y66 ×××××××× ww66+ yy55 ××××××××ww55 + + yy44 ×××××××× ww4 4 + y+ y3 3 ×××××××× ww33 + y+ y22 ×××××××× ww22
+ + yy11×××××××× ww11 + + yy00 ×××××××× ww0 0
00 , , ……………… (3)(3)
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
7536 Code
�� At place = 3, weight is 7At place = 3, weight is 7
�� At place = 2, weight is 5At place = 2, weight is 5
�� At place = 1, weight is 3At place = 1, weight is 3
�� At place = 0, weight is At place = 0, weight is ––66
�� y = 0 or 1y = 0 or 1
![Page 17: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/17.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
7536 Code
�� At place = 4, weight is 10 At place = 4, weight is 10 ×××××××× ww0
�� At place = 5, weight is 10 At place = 5, weight is 10 ×××××××× ww1
�� At place = 6, weight is 10 At place = 6, weight is 10 ×××××××× ww2
�� At place = 7, weight is 10 At place = 7, weight is 10 ×××××××× ww3
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Outline• BCD Code• Excess 3-Code BCD Code• 7536 code• 2421 code• 5421 code
![Page 19: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/19.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
2421 Code
• Formula is N = yy7 7 ×××××××× ww77 + y+ y66 ×××××××× ww66+ yy55 ××××××××ww55 + + yy44 ×××××××× ww4 4 + y+ y3 3 ×××××××× ww33 + y+ y22 ×××××××× ww22
+ + yy11×××××××× ww11 + + yy00 ×××××××× ww0 0
00 , , ……………… (3)(3)
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
2421 Code
�� At place = 3, weight is 2At place = 3, weight is 2
�� At place = 2, weight is 4At place = 2, weight is 4
�� At place = 1, weight is 2At place = 1, weight is 2
�� At place = 0, weight is 1At place = 0, weight is 1
�� y = 0 or 1y = 0 or 1
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
2421 Code
�� At place = 4, weight is 10 At place = 4, weight is 10 ×××××××× ww0
�� At place = 5, weight is 10 At place = 5, weight is 10 ×××××××× ww1
�� At place = 6, weight is 10 At place = 6, weight is 10 ×××××××× ww2
�� At place = 7, weight is 10 At place = 7, weight is 10 ×××××××× ww3
![Page 22: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/22.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Outline• BCD Code• Excess 3-Code BCD Code• 7536 code• 2421 code• 5421 code
![Page 23: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/23.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
5421 Code
• Formula is N = yy7 7 ×××××××× ww77 + y+ y66 ×××××××× ww66+ yy55 ××××××××ww55 + + yy44 ×××××××× ww4 4 + y+ y3 3 ×××××××× ww33 + y+ y22 ×××××××× ww22
+ + yy11×××××××× ww11 + + yy00 ×××××××× ww0 0
00 , , ……………… (3)(3)
![Page 24: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/24.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
5421 Code
�� At place = 3, weight is 2At place = 3, weight is 2
�� At place = 2, weight is 4At place = 2, weight is 4
�� At place = 1, weight is 2At place = 1, weight is 2
�� At place = 0, weight is 1At place = 0, weight is 1
�� y = 0 or 1y = 0 or 1
![Page 25: Digital Design: CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS](https://reader034.fdocuments.us/reader034/viewer/2022042701/55c52f73bb61eb82638b4850/html5/thumbnails/25.jpg)
Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
5421 Code
�� At place = 4, weight is 10 At place = 4, weight is 10 ×××××××× ww0
�� At place = 5, weight is 10 At place = 5, weight is 10 ×××××××× ww1
�� At place = 6, weight is 10 At place = 6, weight is 10 ×××××××× ww2
�� At place = 7, weight is 10 At place = 7, weight is 10 ×××××××× ww3
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Summary
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
Decimal Number representation codes
� 8241 code� XS-3 code� 7536, 2421 and 5421 codes
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
End of Lesson 1
Decimal Number Codes
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Ch11L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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