Built-in Test with Modified-Booth High-Speed Pipelined Multipliers and Dividers

An embedded test pattern generator scheme for large-operand (unlimited bit length) multiplier and divider is presented by employing a simple digital circuit. This scheme is based on the generation of cyclic code polynomials from a characterized polynomials generator G(X) and incorporated with Modified-Booth algorithm. Due to the advantages of the former, the hardware complexity is simple, and moreover, the multiplier and divider can share the same hardware with a small change of control lines. Due to the advantages of latter's schemes, the numbers of “sub/add” operations are reduced to one half of the multiplicand for the result of final product. Therefore, the proposed pipelined multipliers permit very high throughput for arbitrary value of digit size. Only full adders/subtractors and shift registers are used in the proposed multiplier and divider hardware. The input data of the multiplier/divider can be processed in parallel or in pipelined without considering carry/borrow delays during the operations. The speed of computation has therefore been greatly improved by approximately a factor of 2. Since most parts of the components can be used for both the multiplier and divider, with full adders replaced by subtractors for switching from a multiplier to a divider, the structure is therefore tremendously reduced. In addition, these function units are involved with cyclic code generators, so that they can be used as a built-in self-test (BIST).