A seven segment decoder is typically used to determine which light emit- ting diodes in a seven segment display should illuminate to display a digit specified in binary coded decimal. S0 S1 S2 S3 Logisim includes such a seven segment display that you will use in this question. The decoder takes as input four binary bits, which we label in order from most significant bit to least significant bit, A3 A2 A1 A0. The decoder produces as output a pattern of 7 bits, S6 S5 S4 S3 S2 S1 S0, which specifies which segments should illuminate. The figure on the right shows the relationship between the pins and the corresponding seg- ments of the display. Note that there is an 8th pin, S7, which controls the decimal point and that we will not use in this assignment. S1 S3 SO S4 S6 S5 S7 In this question, Instead of decoding BCD, your decoder should produce letters A through J for binary bit patterns zero through 9, and can produce any output (i.e, we don't care) for binary bit patterns 10 through 15. Your decoder should produce exactly the patterns shown below. S4 S5 S6 S7 1. Write out a truth table for vour circuit and include this with vour written answers. 2. Implement the 7 boolean functions in the provided logisim circuit file using only AND, OR and NOT gates provided in the built in library (it is also OK to use NAND and NOR gates, and to negate inputs on gates). You may use any solution you wish, but you may find it easiest to use a sum of products approach, much like a PLA