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Chapter 11Chapter 11

CODES, CONVERTERS,

COMPARATORS, AND LOGIC

OPERATION PROCESSINGCIRCUITS

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Lesson 1

Decimal Number Codes

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Outline BCD (8421) code

Excess 3-Code BCD Code 7536 code

2421 code

5421 code

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yypmaxpmax 11

ww00

pmaxpmax 11 + y+ ypmaxpmax 22

ww00pmaxpmax 22

yypmaxpmax 33 x wx w00pmaxpmax 33

++. +. + yy22

ww0022

+ y+ y11

ww0011

++ yy00 ww0000 ,, . (1). (1)

General Formula N = sum of the yp (Base)p

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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), (pmax3), (pmax 2) or (pmax2) or (pmax 1), from right1), from rightto leftto left

pmax = maximum the number of placespmax = maximum the number of placesused 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

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8421 code Place value and base8421 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

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8421 code Place value and base8421 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

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Outline BCD Code

Excess 3-Code BCD Code 7536 code

2421 code

5421 code

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Excess 3-Code (XS-3) BCD Code

Start not from 0 but from 0011

Formula is N = 3 + yypmaxpmax 11 ww00pmaxpmax 11 ++

yypmaxpmax 22

ww00pmaxpmax 22

yypmaxpmax 33 x wx w00pmaxpmax

33 ++. +. + yy22 ww0022 + y+ y11 ww00

11 ++

yy00 ww0000 ,, . (2). (2)

y = 0 or 1 in binary formy = 0 or 1 in binary form

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XSXS--3 code Place value and base3 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

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XSXS--3 code Place value and base3 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

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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 decimalnumber 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-3code for 0 is 0100 and for 8 it is 1011

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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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Outline BCD Code

Excess 3-Code BCD Code 7536 code

2421 code

5421 code

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7536 Code

Formula is N = yy77 ww77 + y+ y66 ww66+ yy55 ww55 ++ yy44 ww44 + y+ y33 ww33 + y+ y22 ww22

++ yy11

ww

11 ++

yy

00

ww

00

00

,,

(3)(3)

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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 isAt place = 0, weight is 66

y = 0 or 1y = 0 or 1

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7536 Code

At place = 4, weight is 10At place = 4, weight is 10 ww0

At place = 5, weight is 10At place = 5, weight is 10 ww1

At place = 6, weight is 10At place = 6, weight is 10 ww2

At place = 7, weight is 10At place = 7, weight is 10 ww3

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Outline

BCD Code

Excess 3-Code BCD Code 7536 code

2421 code 5421 code

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2421 Code

Formula is N = yy77 ww77 + y+ y66 ww66+ yy55 ww55 ++ yy44 ww44 + y+ y33 ww33 + y+ y22 ww22

++ yy11 ww

11++ yy

00 ww

00

00 ,, (3)(3)

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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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2421 Code

At place = 4, weight is 10At place = 4, weight is 10 ww0

At place = 5, weight is 10At place = 5, weight is 10 ww1

At place = 6, weight is 10At place = 6, weight is 10 ww2

At place = 7, weight is 10At place = 7, weight is 10 ww3

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Outline

BCD Code

Excess 3-Code BCD Code 7536 code

2421 code 5421 code

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5421 Code

Formula is N = yy77 ww77 + y+ y66 ww66+ yy55 ww55 ++ yy44 ww44 + y+ y33 ww33 + y+ y22 ww22

++ yy11 ww

11++ yy

00 ww

00

00 ,, (3)(3)

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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

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5421 Code

At place = 4, weight is 10At place = 4, weight is 10 ww0

At place = 5, weight is 10At place = 5, weight is 10 ww1

At place = 6, weight is 10At place = 6, weight is 10 ww2

At place = 7, weight is 10At place = 7, weight is 10 ww3

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Summary

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Decimal Number representationcodes

8241 code XS-3 code

7536, 2421 and 5421 codes

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End of Lesson 1

Decimal Number Codes

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THANK YOU