A modulo 10 adder is needed for adding BCD digits. Modulo 10 addition of two BCD digits, A = A3A2A1A and B = B3B2B Bo, can be achieved as follows: Add A to B (binary addition). Then, if the result is an illegal code that is greater than or equal to 1010, add 610. (Ignore overflow from this addition.)

(a) When is the output carry equal to 1?

(b) Show that this algorithm gives correct results for

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(1) A 0101 and (2) A 0011 and B = 0110 B = 0100