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1. Design a digital combinational circuit which compares two 2-bit binary numbers and produces results using a 2-bit binary number (please see the block diagram below). The output Z1Z0 depends on the inputs A1A0 and B1B0 according to the following criteria:
If (A1A0 > B1B0) the output Z1Z0 = 10
If (A1A0 B1B0) the output Z1Z0 = 01
If (A1A0 = B1B0) the output Z1Z0 = 11
You should use minimum number of logic gates.

2. Using basic Boolean algebra identities, prove that ABC+ABC’+AB’C+A’BC = AB + AC + BC. Please show all steps and mention the identities used.

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