Question

Design a bcd-to-decimal decoder using the unused combinations of the bcd code as don't-care conditions.

Answer 1

The 74HC/HCT42 are BCD to decimal decoders. These decoders accept four active HIGH BCD inputs and provide 10 mutually exclusive active LOW outputs. The active LOW outputs facilitate addressing other MSI circuits with active LOW input enables. They are pin compatible with low power Schottky TTL (LSTTL). They are specified in compliance with JEDEC standard no. 7A.

The logic design of the '42' ensures that all outputs are HIGH when binary codes greater than nine are applied to the inputs.

The most significant input (A3) produces an useful inhibit function when the '42' is used as a 1-of-8 decoder. The A3 input can also be used as the data input in an 8-output demultiplexer application.

Features

Mutually exclusive outputs 

1-of-8 demultiplexing capability 

Outputs disabled for input codes above nine 

Output capability: standard 

ICC category: MSI 

Applications 

Driving LED displays 

Driving incandescent displays 

Driving fluorescent displays 

Driving LCD displays 

Driving gas discharge displays

Answer 2

FIND: Design a bcd-to-decimal decoder using the unused combinations of the bcd code as don't-care conditions.

Explanation:

step 1:

Draw a truth table for bcd to decimal decoder. table is attached herewith.

In truth table:  

                     A B C D are BCD input values.

                     D₀ to D₉ are decimal output values.

step 2:

Now draw K-map for this truth table as shown in figure enclosed herewith.

step 3:

Now D₁₀ to D₁₅ are unused states. so we will consider them as don't care condition and marks those states as "× " in K-map.

now do the grouping in K-map and find the expression for D₀ to D₉. Grouping is shown in figure enclosed herewith.

D₀ = A'B'C'D'

D₀ =  A'B'C'D'

D₁ =  A'B'C'D

D₂ =  B'CD'

D₃ =  B'CD

D₄ =  BC'D'

D₅ =  BC'D

D₆ =  BCD'

D₇ =  BCD

D₈ =  AD'

D₉ =  AD

It is all about designing part.

Further we can draw its logical diagram also by using ABCD as input lines.