A Formal Proof of PG Recurrence Equations of Parallel Adders

Parallel adders are extensively used in high performance computer design and hardware acceleration for large-scale data processing. In the adder design theory, a key property of the group propagated carry and the group generated carry is based on the two recurrence equations. The property is fundamental to many parallel prefix adders. However, there is no proof of the property in the literature. This paper presents a rigorous and complete proof for it. The proof can leverage a solid ground for a formal verification methodology for parallel adder-based chip design

Effects of Fermented Bamboo Powder Supplementation on Serum Biochemical Parameters, Immune Indices, and Fecal Microbial Composition in Growing–Finishing Pigs

This experiment aimed to investigate the effects of fermented bamboo powder (FBP) on the growth performance, serum biochemical parameters, immunoglobulins and inflammatory cytokines, and fecal microbial composition of growing–finishing pigs. A total of 108 barrows (initial body weight, 56.30 ± 0.55 kg) were randomly allocated to three dietary treatments in a 75 d trial, including a control (CON) diet and two FBP supplementation diets. The CON diet was formulated to three-phase diets according to the body weight of pigs, and the FBP diets were formulated used 5.00% (FBP1) or 10.00% (FBP2) FBP to replace the wheat bran in the CON diet, respectively. The results showed that there were no influences on growth performances between the CON diet and FBP addition diets, whereas the 5% FBP addition decreased the feed:gain of pigs compared to the pigs fed the FBP2 diet from d 0–75 (p < 0.05). Meanwhile, the FBP addition increased the high-density lipoprotein cholesterol (HDLC) and immunoglobulin A (IgA) content in serum (linear, p < 0.05), and pigs fed the FBP1 diet had greater HDLC and IgA contents in serum than those in the pigs fed the CON diet (p < 0.05). Microbial analysis showed that the FBP addition diets decreased the abundance of Spirochaetes, and the FBP2 diet increased the abundance of Firmicutes more than the CON diet (p < 0.05). In addition, the pigs fed the FBP2 diet increased the abundance of uncultured_bacterium_f_Lachnospiraceae, Ruminococcaceae_UCG-005, Prevotellaceae_UCG-003, Lachnospiraceae_XPB1014_group, and Lactobacillus more than the CON group (p < 0.05). In conclusion, the FBP supplementation to the diet had no negative effects on the growth performance and exerted beneficial effects on promoting serum biochemical and immune indices, as well as modulating the fecal microbiota of pigs. Therefore, these results showed that the fermented bamboo powder could be one potential fiber-rich ingredient for growing–finishing pigs, and that the recommended addition proportion in the growing–finishing pigs’ diet is 5%