Problem $1.$ Consider computing $\backslash ((-3/8)^\{2\}=(1\mathrm{.}101)^\{2\}\backslash )$ using the shift$-$and$-$add multiplier for signed numbers similar to that discussed in lecture. Both the multiplicand, $\backslash (1\mathrm{.}101\_\{\backslash$text $\{$two $\}\}\backslash ),$ and multiplier, $\backslash (1\mathrm{.}101\_\{\backslash$text $\{$two $\}\}\backslash ),$ are $4-$bit signed binary integers in two's complement representation. Assume an $8-$bit product register and an adder with the appropriate number of bits. The multiplier is initially loaded in the least significant $4$ bits of the product register and shifts are to the right.

Compute the product using this shift$-$and$-$add multiplier. Show the initial contents of the product register. Do the multiplication. For each iteration identify all arithmetic and shift operations. Show the contents of the product register after each iteration. Clearly and unambiguously identify the final result and indicate the where the binary point is located.