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An encoder is a combinational logic circuit that essentially performs the opposite function of the decoder circuit. An encoder accepts an active level (i.e. ‘1’) on one of its inputs representing a digit (e.g. decimal or octal digit) and converts it to a coded output (e.g. binary of BCD). The process of converting from familiar symbols or numbers to a coded format is called encoding.

The Decimal-to-BCD Encoder

Recall that with BCD the ten decimal digits (0,1,…,9) are represented by their four-digit binary counterparts. Consequently, we expect the Decimal-to-BCD encoder to have 10 inputs and 4 outputs. The logic symbol for this 10-line-to-4-line decoder is presented in Figure 2-11 and the associated conversion table listed in Table 2-13 with A₃ representing the most significant bit.

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Figure 2-11 Logic symbol for Decimal-to-BCD Encoder

Decimal Digit	BCD Code
Decimal Digit	A₃	A₂	A₁	A₀
0	0	0	0	0
1	0	0	0	1
2	0	0	1	0
3	0	0	1	1
4	0	1	0	0
5	0	1	0	1
6	0	1	1	0
7	0	1	1	1
8	1	0	0	0
9	1	0	0	1

Table 2-13 Decimal-to-BCD code table

Now, note that the MSB is defined by the function

A₃= 8 + 9

Similarly, A₂, A₁ and A₀ are defined by the functions

A₂= 4 + 5 + 6 + 7

A₁= 2 + 3 + 6 + 7

A₀= 1 + 3 + 5 + 7 + 9

Now we can implement the logic circuit for the decimal-to-BCD-decoder as illustrated in Figure 2-12.

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Figure 2-12 Logic circuit for Decimal-to-BCD encoder

Note that a connection for the decimal digit zero is not required as in this case the BCD outputs are all LOW when there are no HIGH inputs.

Can you identify any applications where encoders are used?