comparators & code converter ppt

Alpha Breathing

Evocation

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Code Converters

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BCD-to-Excess-3 Code Converter - Specificaiton

The excess-3 code for a decimal digit is the binary combination correspondingto the decimal digit plus 3. For example, the excess-3 code for decimal digit 5is the binary combination for 5 + 3 = 8, which is 1000.

Each BCD digit is four bits with the bits, from most significant to leastsignificant, labeled A, B, C, D. Each excess-3 digit is four bits, with the bits,from most significant to least significant, labeled W, X, Y, Z.

ABCD

WXYZ

BCDdigit

Excess-3digit

BCD-toExcess-3

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BCD-to-Excess-3 Code Converter - Formulation

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BCD-to-Excess-3 Code Converter - Optimization

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BCD-to-Excess-3 Code Converter - Optimization

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BCD-to-Seven-Segment Decoder - Specification

Digital readouts found in many consumer electronic products often use LightEmitting Diodes (LEDs). Each digit of the readout is formed from seven LEDsegments. Each segment can be illuminated by a digital signal. A BCD-to-

seven-segment decoder is a combinational circuit that accepts a decimal digit inBCD and generates the appropriate outputs for the segments of the displayfor the decimal digit. The seven outputs of the decoder (a,b,c,d,e,f,g)select the corresponding segments in the display. BCD-to-seven-segmentdecoder has four inputs, A, B, C, and D for the BCD digit and seven outputs,a through g, for controlling the segments.

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BCD-to-Seven-Segment Decoder - Formulation

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BCD-to-Seven-Segment Decoder - Optimization

a= A’C + A’BD + B’C’D’ + AB’C’

b= A’B’ + A’C’D’ + A’CD + AB’C’

c= A’B + A’D + B’C’D’ + AB’C’

d= A’C^D’ + A’B’C + B’C’D’ + AB’C’ + A’BC’D

e= A’CD’ + B’C’D’

f= A’BC’ + A’C’D’ + A’BD’ + AB’C’

g= A’CD’ + A’B’C + A’BC’ + AB’C’

FOUR BIT BINARY TO GRAY CODE CONVERTER –DESIGN

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INPUT ( BINARY)   OUTPUTS (GRAY CODE)

B3 B2 B1 B0   G3 G2 G1 G0

0 0 0 0   0 0 0 0

0 0 0 1   0 0 0 1

0 0 1 0   0 0 1 1

0 0 1 1   0 0 1 0

0 1 0 0   0 1 1 0

0 1 0 1   0 1 1 1

0 1 1 0   0 1 0 1

0 1 1 1   0 1 0 0

1 0 0 0   1 1 0 0

1 0 0 1   1 1 0 1

1 0 1 0   1 1 1 1

1 0 1 1   1 1 1 0

1 1 0 0   1 0 1 0

1 1 0 1   1 0 1 1

1 1 1 0   1 0 0 1

1 1 1 1   1 0 0 0

MSB0

+1

+1

+0

+1

0 1 0 1 1

Binary code

Gray code

Simplification using K-maps

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Logic Diagram

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FOUR BIT GRAY CODE TO BINARY CONVERTER –DESIGN

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INPUT ( GRAY CODE)   OUTPUTS (BINARY )

G3 G2 G1 G0   B3 B2 B1 B0

0 0 0 0   0 0 0 0

0 0 0 1   0 0 0 1

0 0 1 0   0 0 1 1

0 0 1 1   0 0 1 0

0 1 0 0   0 1 1 1

0 1 0 1   0 1 1 0

0 1 1 0   0 1 0 0

0 1 1 1   0 1 0 1

1 0 0 0   1 1 1 1

1 0 0 1   1 1 1 0

1 0 1 0   1 1 0 0

1 0 1 1   1 1 0 1

1 1 0 0   1 0 0 0

1 1 0 1   1 0 0 1

1 1 1 0   1 0 1 1

1 1 1 1   1 0 1 0

MSB1

+0

+1

+0

+0

1 1 0 0 0

Gray code

Binary code

Puzzles

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MIND MAP

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Summary

Code Converters

Truth tableK-MapExcitation EquationLogic Diagram

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