I need to construct a `combinational circuit`

for the below `truth table`

using a `decoder`

and a `OR`

gate. I'm familiar with the normal procedure of drawing `combinational circuit diagrams`

but got confused when I saw **"using a decoder"** part.

According to the `truth table`

it should be a `4X16 decoder`

. But How Can I mark the 16 outputs of the `decoder`

with respective to the truth table's `sum of production`

??? I know how to use `OR`

gate in this question, but implementing the outputs of the `decoder`

is the problem.

## Best Answer

The decoder is a given. It is takes 4 inputs, and has 16 outputs. Outputs could be labeled 0 to 15. For any combination of inputs exactly one of the outputs will go high. Draw a block with 4 inputs on the left and 16 outputs on the right. That is given in the setup to the problem. For example, a 74LS154 IC is a decoder (but the outputs are active low).

The exercise is about combining the decoder and OR gates to get the output shown in the question.