Encoder is a combinational circuit
which converts one of its active input lines into corresponding binary
number. Encoder performs reverse
operation of decoder. It consist of 2

^{n}input lines and produces n-bit output.
8
to 3 encoder:

Boolean equations for encoder is

A=D1+D3+D5+D7

B=D2+D3+D6+D7

C=D4+D5+D6+D7

__8 to 3 priority encoder:__

In a normal encoder, at a time
only one input should be in active state. Otherwise the output of encoder is
not correct. For example if D3 and D4 both are active then output of encoder is
111(i.e. 7), which is not equal to either 3 or 4. To avoid this problem
priority encoder is used.

In above truth table x indicates
don’t care. D7 has highest priority and priority decreases from D6 to D0. If D7
is 1, then irrespective of other inputs output is 111(i.e. 7). If D5 is 1 and
D6, D7 both are 0’s then output is 101(i.e. 5). GS output means ‘got
something’. If any of the input to encoder is active then GS becomes 1. If all
the inputs to encoder are 0’s then GS is 0.

The Boolean equations for above
priority encoder are

B2=D4+D5+D6+D7

B1=D7+D6+D5’ D4’ (D3+D2)

B0=D7+D6’D5+D6’D4’D3+D6’D4’D2’D1

GS=D0+D1+D2+D3+D4+D5+D6+D7

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