32-Bit

Memory, as well as other digital circuits and wiring, was expensive during the first decades of 32-bit architectures (the 1960s to the 1980s). Older 32-bit processor families (or simpler, cheaper variants thereof) could therefore have many compromises and limitations in order to cut costs. This could be a 16-bit ALU, for instance, or external (or internal) buses narrower than 32 bits, limiting memory size or demanding more cycles for instruction fetch, execution or write back.
Despite this, such processors could be labeled "32-bit," since they still had 32-bit registers and instructions able to manipulate 32-bit quantities. For example, the original Motorola 68000 had a 16-bit data ALU and a 16-bit external data bus, but had 32-bit registers and a 32-bit based instruction set. Such designs were sometimes referred to as "16/32-bit".
However, the opposite is often true for newer 32-bit designs. For example, the Pentium Pro processor is a 32-bit machine, with 32-bit registers and instructions that manipulate 32-bit quantities, but the external address bus is 36 bits wide, giving a larger address space than 4 GB, and the external data bus is 64 bits wide, primarily in order to permit a more efficient prefetch of instructions and data.

 Courtesy of Wikipedia

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