cs281_lec11
... equivalent, e.g. 4 ≡ -4 (mod 8), etc… • Binary addition in k bits is equivalent to addition in Z2k ring. • In k-bits, the largest number will be = 011…11 = 2k-1-1 • In k-bits, the smallest number will be = 100…00 = -2k-1 • Representation: bk-1…b0 = -bk-12k-1+bk-22k-2+…b121+b020 Lec 11 ...
... equivalent, e.g. 4 ≡ -4 (mod 8), etc… • Binary addition in k bits is equivalent to addition in Z2k ring. • In k-bits, the largest number will be = 011…11 = 2k-1-1 • In k-bits, the smallest number will be = 100…00 = -2k-1 • Representation: bk-1…b0 = -bk-12k-1+bk-22k-2+…b121+b020 Lec 11 ...
Mathematics and architecture
Mathematics and architecture are related, since, as with other arts, architects use mathematics to shape and sometimes to decorate buildings.In ancient Greece, buildings were laid out with specific proportions. In Islamic architecture, geometric shapes and geometric tiling patterns are used. The pyramids of ancient Egypt have mathematical proportions. Hindu temples have a fractal-like structure where parts resemble the whole.In Renaissance architecture, symmetry and proportion were deliberately emphasized.In the twentieth century, styles such as modern architecture and Deconstructivism explored different geometries to achieve desired effects.