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You are given a design board with two 4-bit input pins A and B and two output pins: a 4-bit Q and a 1-bit R. Build from gates a circuit that computes (A + B)/2 and asserts it on pin Q. The remainder from the division should be asserted on pin R. For example, if the input is 4 and 2, the output should be 3 for Q and 0 for R, and if the input is -5 and -2, your circuit should assert -4 on Q and 1 on R. Assume that A and B are 2's complement numbers. Your solution should produce the correct result for any values of A and B.