Problem 2. (30 Points] a) Let a2aja, and babybo be 3-bit binary numbers, where a2 and b2 are the most significant bits and ao and bo are the least significant bits. Write a Boolean formula in propositional logic (not boolean algebra) that evaluates to true if a2a1a0 >= b2bibo, and false otherwise (>= means greater than equal). Requirement: Your final answer should only use OR, AND, inverters (-) or XOR (e). Any other answers should be reduced to a format with only OR, AND, inverters or XOR. You may not need to use all of the allowed operators in your answer. Hint: You should compare the two numbers bit by bit. Make some concrete cases to group many cases in one group. For example, you can group (100, 011), (101, 011) and (101, 010) in one group because in all of them a2 >b2. b) Let ajao, bibo and cico be 2-bit binary numbers, and let e3e2ejeo = ajao + bibo + cico be a 4-bit binary number. For example, 0110 = 10+11+01. Write boolean expressions in propositional logic (not boolean algebra) for eo and ez. You should also be able to write a formula for ei and e2 but no need to submit it. Requirement: Your final answer for eo should only use inverters (-) or XOR (e). Your final answer for ez should only use OR, AND, inverters (-) or XOR (e). Any other answers should be reduced to a requested format. You may not need to use all of the allowed operators in your answer. Hint: Look at problem 3 in discussion 3 for some help. c) Let 04230201 ao be an 5-bit binary number. Write a boolean formula in propositional logic (not boolean algebra) that evaluates to true if either an odd number of bits of this number is 1 or it is a non-zero even number but not both, and false otherwise. Requirement: Your final answer should only use OR, AND, inverters () or XOR (e). Any other answers should be reduced to the requested format. You may not need to use all of the allowed operators in your