Functional redundancy 0/ an adder Consider the adder of Example 8.1 in section 8.2.1.1 : C = A + B ('+' is here the addition operator).

1. We suppose that inputs A and Bare two one-digit decimal numbers, and that all (A, B) combinations have the same occurrence probability. We want to analyze the probabilistic functional redundancy of this circuit.

Draw the probabilistic output functional domain and deduce the existing functional redundancy. How can this information be used to detect calculation errors?

2. The two numbers A and B are now in Natural Binary Coded Decimal

(with 4 bits) : 0 = (0000), 1 = (0001), .. . , 9 = (1001). Knowing that the inputs have the same probability, determine the input and the output functional redundancy rates of this system.

3. We suppose now that the two input numbers are binary with two bits, and that an extern al constraint exists between these numbers: A $; B.

Determine the input functional redundancy of this product.