An M-bit thermometer code for the number k consists of k 1's in the least significant bit positions and M - k 0's in all the more significant bit positions. A binary-to-thermometer code converter has N inputs and 2N-1 outputs. It produces a 2N-1 bit thermometer code for the number specified by the input. For example, if the input is 000, the output should be 0000000; if the input is 001, the output should be 0000001; if the input is 010, the output should be 0000011; ... ; if the input is 110, the output should be 0111111; if the input is 111, the output should be 1111111. Design a 3:7 binary-to-thermometer code converter. Give a simplified Boolean equation for each output, and sketch a schematic.