Why do some 3 to 5 decoders only have certain inputs decoded?

[alvinliu]

I don't know why they circle the 001 .011. 100.101. 110 .because I saw the textbook showed for 3to 4 decoder. Y0 =1 since 00. Y1 = 1 since 01. Y2 =1 since 10,Y3 = 1 since 11.

But for this problem . I am so confused.

 

[NascentOxygen]

My guess is that the need was for an output only for the listed 3-bit inputs. Other states come under the "don't care" category. All that is required in the 'design' process is to find a unique combination of bits on the input (the fewer the better) to generate each of those required outputs. There is more than one valid design. e.g., an alternative which won't conflict with any of the other decoding appears to be Y₁=I₁.and.I₀

There would be plenty of applications where they'd want every input decoded to an output, so none of these shortcuts would be possible.

The EN signal looks like an ENABLE line.