# Decimal To BCD Encoder In Digital Electronics

A decimal to bcd encoder has 10 input lines D0 to D9 and 4 output lines Y0 to Y3. Below is the truth table for a decimal to bcd encoder.

From the truth table, the outputs can be expressed by  following Boolean Function.

Note: Below boolean functions are formed by ORing all the input lines for which output is 1. For instance Yis 1 for D1, D3, D5, D7 & D9 input lines.

Y = D1 + D3 + D5 + D7 + D9

Y = D2 + D3 + D6 + D7

Y = D4 + D5 + D6 + D7

Y = D8 + D9

The decimal to bcd encoder can therefore be implemented with OR gates whose inputs are determined directly from truth table as shown in the image below.

#### Limitations With Decimal To BCD Encoder

A decimal to bcd encoder has limitations similar to octal to binary encoder.

1. For 10 bits input, there can be 210 possible combinations, out of which only 10 are used using 4 output lines.
2. The discrepancy of 0 output due to all inputs being 0 or D0 being 0 is resolved by using additional input known as Enable
3. Only one input can be active at any given time.

We will learn about Priority Encoders in next post.

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