Design a circuit with four inputs and four outputs (numbered 1 to 4) that satisfies the following conditions:

The circuit should compute how many of the inputs are 1. If only one of the inputs is 1 , output number 1 must be 1 and the other outputs are 0 . If two inputs are 1 then the first two outputs must be 1 , and so on. Therefore, if all inputs are 1 then all outputs will be 1 as well. You need to construct two-level Boolean expressions for each of the outputs and then try to use these expressions to obtain a multi-level implementation of the whole circuit that is as compact as possible.