Question

Consider the expression (a - 1)* (((b+c)/3)+d)). Let X be the minimum number of registers required by an optimal code generation (without any register spill) algorithm for a load/store architecture, in which (i) only load and store instructions can have memory operands and (ii) arithmatic instructions can have only register or immediate operands. The value of X is

Answer 1

Let $T_{1}and{T}_2$ be two registers,
$T_1\leftarrow$ b
$T_2\leftarrow$ c
$T_1\leftarrow$ $(T_1+T_2$)
$T_1\leftarrow$ $T_1$ / 3
$T_2\leftarrow d$
$T_1\leftarrow$ $T_1+T_2$
$T_2\leftarrow$ a
$T_2\leftarrow$ $T_2-1$
$T_1\leftarrow$ $T_1\ast T_2$
Hence only 2 registers are required.