Design a circuit which will multiply a 3-bit binary number CDE by 2, 3, or 5, depending on the value of a 2-bit code AB (00, 01, or 10), to produce a 4-bit result WXYZ. If the result has a value greater than or equal to 15, WXYZ should be 1111 to indicate an overflow. Assume that the code AB = 11 will never occur. Design your circuit using only two-, three-, and four-input NOR gates and inverters. Try to minimize the number of gates required. The inputs A, B, C, D, and E will be available from toggle switches. Any solution which uses 19 or fewer gates and inverters (not counting the five inverters for the inputs) is acceptable.