It is true that memory addresses being twice longer, they take more space. But programs usually do not fill up the memory with addresses. They fill it up with data.
If the processor is 64-bit, just take the 64-bit ISO. x86-64 does not only
allow to use more memory. It has other advantages such as twice more
registers, 64-bit general-purpose registers that allow 64-bit integer
arithmetics: https://en.wikipedia.org/wiki/X86-64#Architectural_features
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