Nearly 50 years ago, Intel created the world’s first commercially produced microprocessor—the 4004 (ref. 1), a modest 4-bit CPU (central processing unit) with 2,300 transistors fabricated using 10 ?m process technology in silicon and capable only of simple arithmetic calculations. Since this ground-breaking achievement, there has been continuous technological development increasing sophisticati...

this paper presents a modified 32-bit rom-based direct digital frequency synthesizer (ddfs). maximum output frequency of the ddfs is limited by the structure of the accumulator used in the ddfs architecture. the hierarchical pipeline accumulator (hpa) presented in this paper has less propagation delay time rather than the conventional structures. therefore, it results in both higher maximum ope...