The primary target architectures of LFS are the AMD/Intel x86 (32-bit) and x86_64 (64-bit) CPUs. On the other hand, the instructions in this book are also known to work, with some modifications, with the Power PC CPU. To build a system that utilizes one of these CPUs, the main prerequisite, in addition to those on the next few pages, is an existing Linux system such as an earlier LFS installation, Ubuntu, Red Hat/Fedora, SuSE, or other distribution that targets the architecture that you have. Also note that a 32-bit distribution can be installed and used as a host system on a 64-bit AMD/Intel computer.
Some other facts about 64-bit systems need to be added here. When compared to a 32-bit system, the sizes of executable programs are slightly larger and the execution speeds are only slightly faster. For example, in a test build of LFS-6.5 on a Core2Duo CPU based system, the following statistics were measured:
Architecture Build Time Build Size 32-bit 198.5 minutes 648 MB 64-bit 190.6 minutes 709 MB
As you can see, the 64-bit build is only 4% faster and is 9% larger than the 32-bit build. The gain from going to a 64-bit system is relatively minimal. Of course, if you have more than 4GB of RAM or want to manipulate data that exceeds 4GB, the advantages of a 64-bit system are substantial.
The default 64-bit build that results from LFS is considered a "pure" 64-bit system. That is, it supports 64-bit executables only. Building a "multi-lib" system requires compiling many applications twice, once for a 32-bit system and once for a 64-bit system. This is not directly supported in LFS because it would interfere with the educational objective of providing the instructions needed for a straightforward base Linux system. You can refer to the Cross Linux From Scratch project for this advanced topic.
There is one last comment about 64-bit systems. There are some older packages that cannot currently be built in a "pure" 64-bit system or require specialized build instructions. Generally, these packages have some embedded 32-bit specific assembly language instructions that fail when building on a 64-bit system. This includes some Xorg drivers for some legacy video cards at http://xorg.freedesktop.org/releases/individual/driver/. Many of these problems can be worked around, but may require some specialized procedures or patches.