{"id":477261,"date":"2023-08-09T09:09:43","date_gmt":"2023-08-09T09:09:43","guid":{"rendered":""},"modified":"2023-09-05T11:14:23","modified_gmt":"2023-09-05T11:14:23","slug":"floating-point-arithmetic","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/in\/wiki\/floating-point-arithmetic\/","title":{"rendered":"\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917 \u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924"},"content":{"rendered":"<p>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u093f\u0902\u0917 \u0915\u0940 \u0926\u0941\u0928\u093f\u092f\u093e \u092e\u0947\u0902 \u090f\u0915 \u092e\u094c\u0932\u093f\u0915 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0939\u0948 \u091c\u094b \u092c\u093e\u0907\u0928\u0930\u0940 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 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\u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948: (-1)^s * m * 2^e, \u091c\u0939\u093e\u0902 &#039;s&#039; \u0938\u093e\u0907\u0928 \u092c\u093f\u091f \u0939\u0948, &#039;m&#039; \u092e\u0939\u0924\u094d\u0935 \u0939\u0948, \u0914\u0930 &#039;e&#039; \u0918\u093e\u0924\u093e\u0902\u0915 \u0939\u0948 .<\/p>\n<h2>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917 \u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0940 \u092a\u094d\u0930\u092e\u0941\u0916 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u0913\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923<\/h2>\n<p>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0908 \u092a\u094d\u0930\u092e\u0941\u0916 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0902 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948 \u091c\u094b \u0907\u0938\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0915\u092e\u094d\u092a\u094d\u092f\u0942\u091f\u0947\u0936\u0928\u0932 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0902:<\/p>\n<ol>\n<li>\n<p>\u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e \u0914\u0930 \u0938\u0940\u092e\u093e: \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0902 \u092c\u0939\u0941\u0924 \u091b\u094b\u091f\u0947 \u0938\u0947 \u0932\u0947\u0915\u0930 \u092c\u0939\u0941\u0924 \u092c\u0921\u093c\u0947 \u092e\u093e\u0928\u094b\u0902 \u0924\u0915, \u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u0940 \u090f\u0915 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964 \u0935\u0947 \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u091a\u094d\u091a \u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0909\u0928\u094d\u0939\u0947\u0902 \u0935\u0948\u091c\u094d\u091e\u093e\u0928\u093f\u0915 \u0914\u0930 \u0907\u0902\u091c\u0940\u0928\u093f\u092f\u0930\u093f\u0902\u0917 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<li>\n<p>\u0935\u0948\u091c\u094d\u091e\u093e\u0928\u093f\u0915 \u0938\u0902\u0915\u0947\u0924\u0928: \u092b\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u0935\u0948\u091c\u094d\u091e\u093e\u0928\u093f\u0915 \u0938\u0902\u0915\u0947\u0924\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092c\u0921\u093c\u0940 \u092f\u093e \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u091c\u0941\u0921\u093c\u0940 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u094b \u0938\u0930\u0932 \u092c\u0928\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p>\u092a\u094b\u0930\u094d\u091f\u0947\u092c\u093f\u0932\u093f\u091f\u0940: IEEE 754 \u092e\u093e\u0928\u0915 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0906\u0930\u094d\u0915\u093f\u091f\u0947\u0915\u094d\u091a\u0930 \u092e\u0947\u0902 \u0938\u0941\u0938\u0902\u0917\u0924 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948, \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0921\u0947\u091f\u093e \u0915\u0940 \u092a\u094b\u0930\u094d\u091f\u0947\u092c\u093f\u0932\u093f\u091f\u0940 \u0914\u0930 \u0907\u0902\u091f\u0930\u0911\u092a\u0930\u0947\u092c\u093f\u0932\u093f\u091f\u0940 \u0915\u094b \u092c\u0922\u093c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p>\u0915\u0941\u0936\u0932 \u0939\u093e\u0930\u094d\u0921\u0935\u0947\u092f\u0930 \u0915\u093e\u0930\u094d\u092f\u093e\u0928\u094d\u0935\u092f\u0928: \u0906\u0927\u0941\u0928\u093f\u0915 \u092a\u094d\u0930\u094b\u0938\u0947\u0938\u0930 \u092e\u0947\u0902 \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0938\u0902\u091a\u093e\u0932\u0928 \u092e\u0947\u0902 \u0924\u0947\u091c\u0940 \u0932\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0936\u0947\u0937 \u0939\u093e\u0930\u094d\u0921\u0935\u0947\u092f\u0930 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0909\u0928\u094d\u0939\u0947\u0902 \u0924\u0947\u091c\u093c \u0914\u0930 \u0905\u0927\u093f\u0915 \u0915\u0941\u0936\u0932 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<li>\n<p>\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935: \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u092e\u0928\u0941\u0937\u094d\u092f\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0924\u0930\u0940\u0915\u0947 \u0915\u0947 \u0938\u093e\u0925 \u0928\u093f\u0915\u091f\u0924\u093e \u0938\u0947 \u0938\u0902\u0930\u0947\u0916\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0938\u0939\u091c \u0938\u092e\u091d \u0914\u0930 \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ol>\n<h2>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917 \u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930<\/h2>\n<p>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u094b \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u092e\u093e\u0928 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u092c\u093f\u091f\u094d\u0938 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e \u092e\u0947\u0902 \u0935\u0930\u094d\u0917\u0940\u0915\u0943\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0938\u092c\u0938\u0947 \u0906\u092e \u092a\u094d\u0930\u0915\u093e\u0930\u094b\u0902 \u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u092a\u094d\u0930\u0915\u093e\u0930<\/th>\n<th>\u092c\u093f\u091f\u094d\u0938<\/th>\n<th>\u092a\u094d\u0930\u0924\u093f\u092a\u093e\u0926\u0915 \u092c\u093f\u091f\u094d\u0938<\/th>\n<th>\u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092c\u093f\u091f\u094d\u0938<\/th>\n<th>\u0936\u094d\u0930\u0947\u0923\u0940<\/th>\n<th>\u0936\u0941\u0926\u094d\u0927\u0924\u093e<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0905\u0915\u0947\u0932\u093e<\/td>\n<td>32<\/td>\n<td>8<\/td>\n<td>23<\/td>\n<td>\u00b13.4 x 10^-38 \u0938\u0947 \u00b13.4 x 10^38<\/td>\n<td>~7 \u0926\u0936\u092e\u0932\u0935 \u0938\u094d\u0925\u093e\u0928<\/td>\n<\/tr>\n<tr>\n<td>\u0926\u094b\u0939\u0930\u093e<\/td>\n<td>64<\/td>\n<td>11<\/td>\n<td>52<\/td>\n<td>\u00b11.7 x 10^-308 \u0938\u0947 \u00b11.7 x 10^308<\/td>\n<td>~15 \u0926\u0936\u092e\u0932\u0935 \u0938\u094d\u0925\u093e\u0928<\/td>\n<\/tr>\n<tr>\n<td>\u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924<\/td>\n<td>\u092d\u093f\u0928\u094d\u0928<\/td>\n<td>\u092d\u093f\u0928\u094d\u0928<\/td>\n<td>\u092d\u093f\u0928\u094d\u0928<\/td>\n<td>\u092d\u093f\u0928\u094d\u0928<\/td>\n<td>\u092d\u093f\u0928\u094d\u0928<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917 \u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0924\u0930\u0940\u0915\u0947, \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928<\/h2>\n<p>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u092e\u0947\u0902 \u092c\u0921\u093c\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u092a\u0930 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0928\u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902:<\/p>\n<ol>\n<li>\n<p>\u0935\u0948\u091c\u094d\u091e\u093e\u0928\u093f\u0915 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u093f\u0902\u0917: \u0938\u093f\u092e\u0941\u0932\u0947\u0936\u0928, \u092e\u0949\u0921\u0932\u093f\u0902\u0917 \u0914\u0930 \u0921\u0947\u091f\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u0905\u0915\u094d\u0938\u0930 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0917\u0923\u0928\u093e \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u0939\u093e\u0902 \u092b\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p>\u0907\u0902\u091c\u0940\u0928\u093f\u092f\u0930\u093f\u0902\u0917: \u091c\u091f\u093f\u0932 \u0907\u0902\u091c\u0940\u0928\u093f\u092f\u0930\u093f\u0902\u0917 \u0938\u093f\u092e\u0941\u0932\u0947\u0936\u0928 \u0914\u0930 \u0921\u093f\u091c\u093c\u093e\u0907\u0928 \u0915\u0947 \u0932\u093f\u090f \u0938\u091f\u0940\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u094b \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p>\u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0917\u094d\u0930\u093e\u092b\u093c\u093f\u0915\u094d\u0938: \u0917\u094d\u0930\u093e\u092b\u093c\u093f\u0915\u094d\u0938 \u092a\u094d\u0930\u094b\u0938\u0947\u0938\u093f\u0902\u0917 \u0930\u0947\u0902\u0921\u0930\u093f\u0902\u0917 \u0914\u0930 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u093c\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0947 \u0932\u093f\u090f \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u092a\u0930 \u092c\u0939\u0941\u0924 \u0905\u0927\u093f\u0915 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ol>\n<p>\u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0928\u0902\u092c\u0930\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0928\u0947 \u0938\u0947 \u0930\u093e\u0909\u0902\u0921\u093f\u0902\u0917 \u0924\u094d\u0930\u0941\u091f\u093f\u092f\u094b\u0902 \u0914\u0930 \u0938\u0940\u092e\u093f\u0924 \u0938\u091f\u0940\u0915\u0924\u093e \u0915\u0947 \u0915\u093e\u0930\u0923 \u091a\u0941\u0928\u094c\u0924\u093f\u092f\u093e\u0901 \u0906 \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964 \u0907\u0938\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0902:<\/p>\n<ul>\n<li>\n<p><strong>\u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e \u0915\u093e \u0928\u0941\u0915\u0938\u093e\u0928<\/strong>: \u092c\u0939\u0941\u0924 \u092c\u0921\u093c\u0947 \u092f\u093e \u092c\u0939\u0941\u0924 \u091b\u094b\u091f\u0947 \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u0915\u0941\u091b \u0917\u0923\u0928\u093e\u0913\u0902 \u092e\u0947\u0902 \u0938\u091f\u0940\u0915\u0924\u093e \u0915\u093e \u0928\u0941\u0915\u0938\u093e\u0928 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><strong>\u0924\u0941\u0932\u0928\u093e<\/strong>: \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0938\u0940\u0927\u0940 \u0924\u0941\u0932\u0928\u093e \u0930\u093e\u0909\u0902\u0921\u093f\u0902\u0917 \u0924\u094d\u0930\u0941\u091f\u093f\u092f\u094b\u0902 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0938\u092e\u0938\u094d\u092f\u093e\u0917\u094d\u0930\u0938\u094d\u0924 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u091b\u094b\u091f\u0947 \u0905\u0902\u0924\u0930\u094b\u0902 \u0915\u094b \u0938\u0902\u092d\u093e\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0908\u092a\u0940\u090f\u0938\u0932\u0949\u0928-\u0906\u0927\u093e\u0930\u093f\u0924 \u0924\u0941\u0932\u0928\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u0936\u0902\u0938\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><strong>\u0938\u093e\u0939\u091a\u0930\u094d\u092f \u0914\u0930 \u0935\u093f\u0924\u0930\u0923<\/strong>: \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0911\u092a\u0930\u0947\u0936\u0902\u0938 \u0915\u093e \u0915\u094d\u0930\u092e \u0930\u093e\u0909\u0902\u0921\u093f\u0902\u0917 \u0924\u094d\u0930\u0941\u091f\u093f\u092f\u094b\u0902 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0905\u0902\u0924\u093f\u092e \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ul>\n<p>\u0907\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0915\u092e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0921\u0947\u0935\u0932\u092a\u0930\u094d\u0938 \u0907\u0928 \u0938\u092e\u093e\u0927\u093e\u0928\u094b\u0902 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul>\n<li>\n<p><strong>\u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0924\u0915\u0928\u0940\u0915\u0947\u0902<\/strong>: \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u0928 \u0924\u094d\u0930\u0941\u091f\u093f\u092f\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u0915\u094b \u0915\u092e \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u0938\u092e\u0917\u094d\u0930 \u0938\u091f\u0940\u0915\u0924\u093e \u092e\u0947\u0902 \u0938\u0941\u0927\u093e\u0930 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><strong>\u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e-\u091c\u093e\u0917\u0930\u0942\u0915 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e<\/strong>: \u0938\u091f\u0940\u0915 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e\u0913\u0902 \u0915\u0947 \u092a\u094d\u0930\u0924\u093f \u0938\u0902\u0935\u0947\u0926\u0928\u0936\u0940\u0932 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0938\u0947 \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u0940 \u0935\u093f\u0936\u094d\u0935\u0938\u0928\u0940\u092f\u0924\u093e \u092c\u0922\u093c \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ul>\n<h2>\u092e\u0941\u0916\u094d\u092f \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901 \u0914\u0930 \u0938\u092e\u093e\u0928 \u0936\u092c\u094d\u0926\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0924\u0941\u0932\u0928\u093e<\/h2>\n<p>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0905\u0915\u094d\u0938\u0930 \u0905\u0928\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0905\u092d\u094d\u092f\u093e\u0935\u0947\u0926\u0928 \u0938\u0947 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u091c\u093f\u0928\u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902:<\/p>\n<ol>\n<li>\n<p><strong>\u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0905\u0902\u0915\u0917\u0923\u093f\u0924<\/strong>: \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924, \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 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\u0932\u093f\u090f \u092d\u093f\u0928\u094d\u0928\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u092c\u093f\u091f\u094d\u0938 \u0915\u0940 \u090f\u0915 \u0938\u094d\u0925\u093f\u0930 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u094b \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e \u0914\u0930 \u0938\u091f\u0940\u0915\u0924\u093e \u0915\u094b \u0938\u0940\u092e\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><strong>\u0926\u0936\u092e\u0932\u0935 \u0905\u0902\u0915\u0917\u0923\u093f\u0924<\/strong>: \u0926\u0936\u092e\u0932\u0935 \u0905\u0902\u0915\u0917\u0923\u093f\u0924, \u091c\u093f\u0938\u0947 \u092e\u0928\u092e\u093e\u0928\u093e-\u0938\u091f\u0940\u0915 \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092d\u0940 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0926\u0936\u092e\u0932\u0935 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092e\u0928\u092e\u093e\u0928\u093e \u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e \u0915\u0947 \u0938\u093e\u0925 \u0938\u0902\u092d\u093e\u0932 \u0938\u0915\u0924\u093e \u0939\u0948 \u0932\u0947\u0915\u093f\u0928 \u092c\u0921\u093c\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u0940 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u092b\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0927\u0940\u092e\u093e \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><strong>\u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u0905\u0902\u0915\u0917\u0923\u093f\u0924<\/strong>: \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0926\u094b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0938\u091f\u0940\u0915 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u091f\u0940\u0915 \u092a\u0930\u093f\u0923\u093e\u092e \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u092f\u0939 \u0905\u092a\u0930\u093f\u092e\u0947\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ol>\n<h2>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917 \u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092d\u0935\u093f\u0937\u094d\u092f \u0915\u0947 \u092a\u0930\u093f\u092a\u094d\u0930\u0947\u0915\u094d\u0937\u094d\u092f \u0914\u0930 \u092a\u094d\u0930\u094c\u0926\u094d\u092f\u094b\u0917\u093f\u0915\u093f\u092f\u093e\u0901<\/h2>\n<p>\u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u093f\u0902\u0917 \u0936\u0915\u094d\u0924\u093f \u0906\u0917\u0947 \u092c\u0922\u093c \u0930\u0939\u0940 \u0939\u0948, \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0947 \u092d\u0935\u093f\u0937\u094d\u092f \u0915\u0947 \u092a\u0930\u093f\u092a\u094d\u0930\u0947\u0915\u094d\u0937\u094d\u092f \u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902:<\/p>\n<ol>\n<li>\n<p><strong>\u0909\u091a\u094d\u091a \u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e<\/strong>: \u0905\u0927\u093f\u0915 \u0938\u091f\u0940\u0915 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u0940 \u092c\u0922\u093c\u0924\u0940 \u092e\u093e\u0902\u0917 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0938\u091f\u0940\u0915 \u092a\u094d\u0930\u093e\u0930\u0942\u092a \u092f\u093e \u0935\u093f\u0936\u0947\u0937 \u0939\u093e\u0930\u094d\u0921\u0935\u0947\u092f\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><strong>\u0915\u094d\u0935\u093e\u0902\u091f\u092e \u0915\u092e\u094d\u092a\u094d\u092f\u0942\u091f\u093f\u0902\u0917<\/strong>: \u0915\u094d\u0935\u093e\u0902\u091f\u092e \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0917\u0923\u0928\u093e \u0915\u0947 \u0932\u093f\u090f \u0928\u0908 \u0924\u0915\u0928\u0940\u0915\u0947\u0902 \u092a\u0947\u0936 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u092b\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u094b \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<li>\n<p><strong>\u092f\u0902\u0924\u094d\u0930 \u0905\u0927\u093f\u0917\u092e<\/strong>: \u090f\u0906\u0908 \u0914\u0930 \u092e\u0936\u0940\u0928 \u0932\u0930\u094d\u0928\u093f\u0902\u0917 \u090f\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u091c\u091f\u093f\u0932 \u092e\u0949\u0921\u0932 \u0914\u0930 \u0921\u0947\u091f\u093e \u0915\u094b \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u093f\u0902\u0917 \u092e\u0947\u0902 \u092a\u094d\u0930\u0917\u0924\u093f \u0932\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<\/ol>\n<h2>\u092a\u094d\u0930\u0949\u0915\u094d\u0938\u0940 \u0938\u0930\u094d\u0935\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u092f\u093e \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917 \u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0938\u0947 \u0938\u0902\u092c\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948<\/h2>\n<p>\u091c\u092c\u0915\u093f \u092a\u094d\u0930\u0949\u0915\u094d\u0938\u0940 \u0938\u0930\u094d\u0935\u0930 \u092e\u0941\u0916\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u0928\u0947\u091f\u0935\u0930\u094d\u0915 \u0938\u0902\u091a\u093e\u0930 \u0915\u094b \u0938\u0941\u0935\u093f\u0927\u093e\u091c\u0928\u0915 \u092c\u0928\u093e\u0928\u0947 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0935\u0947 \u0905\u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u0930\u0942\u092a \u0938\u0947 \u0909\u0928 \u092a\u0930\u093f\u0926\u0943\u0936\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0938\u0947 \u091c\u0941\u0921\u093c\u0947 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0902 \u090f\u0915\u094d\u0938\u091a\u0947\u0902\u091c \u0915\u093f\u090f \u0917\u090f \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092a\u094d\u0930\u0949\u0915\u094d\u0938\u0940 \u0938\u0930\u094d\u0935\u0930 \u0935\u0948\u091c\u094d\u091e\u093e\u0928\u093f\u0915 \u0921\u0947\u091f\u093e, \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092f\u093e \u092e\u0940\u0921\u093f\u092f\u093e \u092b\u093c\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0928\u092e\u0947\u0902 \u0938\u0947 \u0938\u092d\u0940 \u092e\u0947\u0902 \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0928\u0902\u092c\u0930 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923 \u0915\u0947 \u0926\u094c\u0930\u093e\u0928 \u0907\u0928 \u0928\u0902\u092c\u0930\u094b\u0902 \u0915\u0940 \u0938\u091f\u0940\u0915\u0924\u093e \u0914\u0930 \u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0921\u0947\u091f\u093e \u0905\u0916\u0902\u0921\u0924\u093e \u092c\u0928\u093e\u090f \u0930\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0921\u0947\u091f\u093e \u0915\u093e \u0909\u091a\u093f\u0924 \u092a\u094d\u0930\u092c\u0902\u0927\u0928 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0964<\/p>\n<h2>\u0938\u092e\u094d\u092c\u0902\u0927\u093f\u0924 \u0932\u093f\u0902\u0915\u094d\u0938<\/h2>\n<p>\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f, \u0906\u092a \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0938\u093e\u0927\u0928\u094b\u0902 \u0915\u093e \u0938\u0902\u0926\u0930\u094d\u092d \u0932\u0947 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul>\n<li><a href=\"https:\/\/standards.ieee.org\/standard\/754-2019.html\" target=\"_new\" rel=\"noopener nofollow\">\u0906\u0908\u0908\u0908\u0908 754 \u092e\u093e\u0928\u0915<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Floating-point_arithmetic\" target=\"_new\" rel=\"noopener nofollow\">\u0935\u093f\u0915\u093f\u092a\u0940\u0921\u093f\u092f\u093e \u092a\u0930 \u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0905\u0902\u0915\u0917\u0923\u093f\u0924<\/a><\/li>\n<li><a href=\"https:\/\/docs.oracle.com\/cd\/E19957-01\/806-3568\/ncg_goldberg.html\" target=\"_new\" rel=\"noopener nofollow\">\u092b\u093c\u094d\u0932\u094b\u091f\u093f\u0902\u0917-\u092a\u0949\u0907\u0902\u091f \u0917\u093e\u0907\u0921 \u0915\u0947 \u0938\u093e\u0925 \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u093f\u0902\u0917<\/a><\/li>\n<\/ul>","protected":false},"featured_media":468423,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477261","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Floating Point Arithmetic: Understanding the Precision of Numbers in Computing<\/mark>","faq_items":[{"question":"What is floating-point arithmetic?","answer":"<p>Floating-point arithmetic is a fundamental concept in computing that deals with the representation and manipulation of real numbers in a binary form. It allows computers to perform mathematical operations on a wide range of values, including those with fractional parts. The representation involves a significand (mantissa) and an exponent, providing a dynamic format to cover a broader range of magnitudes and precision.<\/p>"},{"question":"How did floating-point arithmetic originate?","answer":"<p>The concept of floating-point arithmetic can be traced back to the early days of computing. It was first mentioned in the pioneering work of Konrad Zuse, a German engineer who developed the Z1 computer in the 1930s. The Z1 utilized a form of floating-point representation to handle decimal numbers and facilitate numerical calculations.<\/p>"},{"question":"How does floating-point arithmetic work?","answer":"<p>Floating-point arithmetic uses the IEEE 754 standard, which specifies formats for single and double precision, as well as operations like addition, subtraction, multiplication, and division. The internal structure involves a sign bit, an exponent, and a significand. The binary representation of a floating-point number can be expressed as (-1)^s * m * 2^e, where 's' is the sign bit, 'm' is the significand, and 'e' is the exponent.<\/p>"},{"question":"What are the key features of floating-point arithmetic?","answer":"<p>Floating-point arithmetic offers several key features that make it essential for various computational tasks. It provides precision and a wide range of representable values, allowing for accurate calculations involving large or small numbers. It employs scientific notation, ensuring efficient handling of significant figures. Moreover, the IEEE 754 standard promotes portability and efficient hardware implementation.<\/p>"},{"question":"What types of floating-point arithmetic exist?","answer":"<p>Floating-point arithmetic is categorized into different precisions based on the number of bits used to represent each floating-point value. The most common types include single precision (32-bit), double precision (64-bit), and extended precision with varying bit sizes.<\/p>"},{"question":"How is floating-point arithmetic used, and what are the challenges?","answer":"<p>Floating-point arithmetic finds applications in scientific computing, engineering, and computer graphics. However, it comes with challenges such as loss of precision, difficulties in direct comparisons, and potential associativity and distributivity issues. To mitigate these problems, developers can use numerical analysis techniques and precision-aware algorithms.<\/p>"},{"question":"How does floating-point arithmetic compare with other numerical representations?","answer":"<p>Floating-point arithmetic is often compared with integer arithmetic, fixed-point arithmetic, decimal arithmetic, and rational arithmetic. Each representation has its advantages and limitations, making floating-point arithmetic suitable for a wide range of applications.<\/p>"},{"question":"What are the future perspectives of floating-point arithmetic?","answer":"<p>As computing power advances, future perspectives for floating-point arithmetic involve higher precision formats and potential impact from quantum computing and machine learning applications.<\/p>"},{"question":"How are proxy servers associated with floating-point arithmetic?","answer":"<p>While proxy servers primarily facilitate network communication, they can indirectly be associated with floating-point arithmetic when transferring data involving real numbers. Ensuring the accuracy and precision of floating-point data during transfer is crucial for maintaining data integrity.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/in\/wp-json\/wp\/v2\/wiki\/477261","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/in\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/in\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/in\/wp-json\/wp\/v2\/wiki\/477261\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/in\/wp-json\/wp\/v2\/media\/468423"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/in\/wp-json\/wp\/v2\/media?parent=477261"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}