An M-bit thermometer code for the number k consists of k 1s in the least significant bit positions and M k 0s in all the more significant bit positions. A binary-to-thermometer code converter has N inputs and 2N1 outputs. It produces a 2N1 bit thermometer code for the number specified by the input. For example, if the input is 110, the output should be 0111111. Design a 3:7 binary-to-thermometer code converter. Give a simplified Boolean equation for each output, and sketch a schematic. Write VHDL code and the test bench. In your test bench, you should include enough number of test cases to show the correctness of your design.