Let's suppose a chain of 6 multipliers: $b = a_1*a_2*a_3*a_4*a_5*a_6*a_7$, where $b$ is the output, and $a_i$ the inputs with 16 bits. How can I optimize the word lengths of the output of each multiplier in order to minimize the fixed point error against a full precision implementation? Let's also suppose that the output $b$ shall be some reasonable word length, for example 35 bits.
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