Encoder

Encoder is reverse of decoder

8-3 encoder

8 inputs, exactly one has value 1

3 output bits, representing which input was equal to 1 (binary representation of input)

Example:

input:

x5 = 1

output:

z2z1z0 = 101

Simplified truth table:

Input == 1

z2

z1

z0

x0

0

0

0

Minterms are rather large

x1

0

0

1

(from full truth table):

x2

0

1

0

z2 = \x0\x1\x2\x3x4\x5\x6\x7 +

x3

0

1

1

\x0\x1\x2\x3\x4x5\x6\x7 +

x4

1

0

0

\x0\x1\x2\x3\x4\x5x6\x7 +

x5

1

0

1

\x0\x1\x2\x3\x4\x5\x6x7

x6

1

1

0

x7

1

1

1

However, we can take advantage of the fact that exactly one input is 1:

z2 = x4 + x5 + x6 + x7

Example:

x5 = 1

z1 = x2 + x3 + x6 + x7

z2z1z0 = 101

z0 = x1 + x3 + x5 + x7

(UB for 5)