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\u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f IEEE 754 \u0631\u0641\u062a\u0627\u0631 \u0645\u0646\u0633\u062c\u0645 \u0631\u0627 \u062f\u0631 \u0645\u0639\u0645\u0627\u0631\u06cc \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0642\u0627\u0628\u0644\u06cc\u062a \u062d\u0645\u0644 \u0648 \u06a9\u0627\u0631\u06a9\u0631\u062f \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u0631\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<\/li>\n<li>\n<p>\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0633\u062e\u062a\u200c\u0627\u0641\u0632\u0627\u0631: \u067e\u0631\u062f\u0627\u0632\u0646\u062f\u0647\u200c\u0647\u0627\u06cc \u0645\u062f\u0631\u0646 \u0634\u0627\u0645\u0644 \u0633\u062e\u062a\u200c\u0627\u0641\u0632\u0627\u0631 \u062a\u062e\u0635\u0635\u06cc \u0628\u0631\u0627\u06cc \u062a\u0633\u0631\u06cc\u0639 \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0633\u0631\u06cc\u0639\u200c\u062a\u0631 \u0648 \u06a9\u0627\u0631\u0622\u0645\u062f\u062a\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n<\/li>\n<li>\n<p>\u0628\u0627\u0632\u0646\u0645\u0627\u06cc\u06cc \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc: \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0627 \u0631\u0648\u0634\u06cc \u06a9\u0647 \u0627\u0646\u0633\u0627\u0646\u200c\u0647\u0627 \u0627\u0639\u062f\u0627\u062f \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u0631\u0627 \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f\u060c \u0647\u0645\u0633\u0648 \u0627\u0633\u062a \u0648 \u0627\u0645\u06a9\u0627\u0646 \u062f\u0631\u06a9 \u0648 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0647\u0648\u062f\u06cc \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0627\u0646\u0648\u0627\u0639 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631<\/h2>\n<p>\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0631 \u0627\u0633\u0627\u0633 \u062a\u0639\u062f\u0627\u062f \u0628\u06cc\u062a \u0647\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0647\u0631 \u0645\u0642\u062f\u0627\u0631 \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0647 \u062f\u0642\u062a \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u0634\u0648\u062f. \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0627\u0646\u0648\u0627\u0639 \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u062a\u0627\u06cc\u067e \u06a9\u0646\u06cc\u062f<\/th>\n<th>\u0628\u06cc\u062a \u0647\u0627<\/th>\n<th>\u0628\u06cc\u062a \u0647\u0627\u06cc \u062a\u0648\u0627\u0646<\/th>\n<th>\u0628\u06cc\u062a \u0647\u0627\u06cc \u0645\u0647\u0645<\/th>\n<th>\u062f\u0627\u0645\u0646\u0647<\/th>\n<th>\u062f\u0642\u062a\u060c \u062f\u0631\u0633\u062a\u06cc<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u062a\u0646\u0647\u0627<\/td>\n<td>32<\/td>\n<td>8<\/td>\n<td>23<\/td>\n<td>3.4 \u00d7 10^-38 \u062a\u0627 3.4 \u00b1 10^38<\/td>\n<td>~ 7 \u0631\u0642\u0645 \u0627\u0639\u0634\u0627\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u062f\u0648 \u0628\u0631\u0627\u0628\u0631<\/td>\n<td>64<\/td>\n<td>11<\/td>\n<td>52<\/td>\n<td>1.7 \u00d7 10^-308 \u062a\u0627 1.7 \u00b1 10^308<\/td>\n<td>~ 15 \u0631\u0642\u0645 \u0627\u0639\u0634\u0627\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0645\u062f\u06cc\u062f \u0634\u062f\u0647<\/td>\n<td>\u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a<\/td>\n<td>\u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a<\/td>\n<td>\u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a<\/td>\n<td>\u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a<\/td>\n<td>\u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0631\u0627\u0647 \u0647\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631\u060c \u0645\u0633\u0627\u0626\u0644 \u0648 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u0622\u0646\u0647\u0627<\/h2>\n<p>\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0647 \u0637\u0648\u0631 \u06af\u0633\u062a\u0631\u062f\u0647 \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f\u060c \u0627\u0632 \u062c\u0645\u0644\u0647:<\/p>\n<ol>\n<li>\n<p>\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0639\u0644\u0645\u06cc: \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc\u060c \u0645\u062f\u0644\u200c\u0633\u0627\u0632\u06cc \u0648 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0627\u063a\u0644\u0628 \u0634\u0627\u0645\u0644 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u0648\u0627\u0642\u0639\u06cc \u0627\u0633\u062a\u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a.<\/p>\n<\/li>\n<li>\n<p>\u0645\u0647\u0646\u062f\u0633\u06cc: \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc\u200c\u0647\u0627 \u0648 \u0637\u0631\u0627\u062d\u06cc\u200c\u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0645\u0647\u0646\u062f\u0633\u06cc \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0646\u0645\u0627\u06cc\u0634 \u0639\u062f\u062f\u06cc \u062f\u0642\u06cc\u0642\u06cc \u062f\u0627\u0631\u0646\u062f \u06a9\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n<\/li>\n<li>\n<p>\u06af\u0631\u0627\u0641\u06cc\u06a9 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc: \u067e\u0631\u062f\u0627\u0632\u0634 \u06af\u0631\u0627\u0641\u06cc\u06a9\u06cc \u0628\u0647 \u0634\u062f\u062a \u0628\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0631\u0627\u06cc \u0631\u0646\u062f\u0631 \u0648 \u062a\u0628\u062f\u06cc\u0644 \u0645\u062a\u06a9\u06cc \u0627\u0633\u062a.<\/p>\n<\/li>\n<\/ol>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u06a9\u0627\u0631 \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0686\u0627\u0644\u0634 \u0647\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u062e\u0637\u0627\u0647\u0627\u06cc \u06af\u0631\u062f \u06a9\u0631\u062f\u0646 \u0648 \u062f\u0642\u062a \u0645\u062d\u062f\u0648\u062f \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u062f. \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0645\u0646\u062c\u0631 \u0628\u0647 \u0645\u0633\u0627\u0626\u0644\u06cc \u0645\u0627\u0646\u0646\u062f:<\/p>\n<ul>\n<li>\n<p><strong>\u0627\u0632 \u062f\u0633\u062a \u062f\u0627\u062f\u0646 \u062f\u0642\u062a<\/strong>: \u0628\u0631\u062e\u06cc \u0627\u0632 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0647\u0646\u06af\u0627\u0645 \u0628\u0631\u062e\u0648\u0631\u062f \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0632\u0631\u06af \u06cc\u0627 \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0648\u0686\u06a9 \u0627\u0632 \u062f\u0642\u062a \u0631\u0646\u062c \u0628\u0628\u0631\u0646\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627<\/strong>: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0627\u0639\u062f\u0627\u062f \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0647 \u062f\u0644\u06cc\u0644 \u062e\u0637\u0627\u0647\u0627\u06cc \u06af\u0631\u062f \u06a9\u0631\u062f\u0646 \u0645\u0634\u06a9\u0644 \u0633\u0627\u0632 \u0628\u0627\u0634\u062f. \u062a\u0648\u0635\u06cc\u0647 \u0645\u06cc \u0634\u0648\u062f \u0627\u0632 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627\u06cc \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u0627\u067e\u0633\u06cc\u0644\u0648\u0646 \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u06af\u06cc \u0628\u0647 \u062a\u0641\u0627\u0648\u062a \u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0646\u062c\u0645\u0646 \u0648 \u062a\u0648\u0632\u06cc\u0639<\/strong>: \u062a\u0631\u062a\u06cc\u0628 \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u062e\u0637\u0627\u0647\u0627\u06cc \u06af\u0631\u062f \u06a9\u0631\u062f\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0646\u0647\u0627\u06cc\u06cc \u062a\u0623\u062b\u06cc\u0631 \u0628\u06af\u0630\u0627\u0631\u062f.<\/p>\n<\/li>\n<\/ul>\n<p>\u0628\u0631\u0627\u06cc \u06a9\u0627\u0647\u0634 \u0627\u06cc\u0646 \u0645\u0634\u06a9\u0644\u0627\u062a\u060c \u062a\u0648\u0633\u0639\u0647 \u062f\u0647\u0646\u062f\u06af\u0627\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0646\u0628\u0627\u0644 \u06a9\u0646\u0646\u062f:<\/p>\n<ul>\n<li>\n<p><strong>\u062a\u06a9\u0646\u06cc\u06a9 \u0647\u0627\u06cc \u062a\u062d\u0644\u06cc\u0644 \u0639\u062f\u062f\u06cc<\/strong>: \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0647\u0627\u06cc \u062a\u062d\u0644\u06cc\u0644 \u0639\u062f\u062f\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062a\u0627\u062b\u06cc\u0631 \u062e\u0637\u0627\u0647\u0627\u06cc \u06af\u0631\u062f \u06a9\u0631\u062f\u0646 \u0631\u0627 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0628\u0631\u0633\u0627\u0646\u062f \u0648 \u062f\u0642\u062a \u06a9\u0644\u06cc \u0631\u0627 \u0628\u0647\u0628\u0648\u062f \u0628\u062e\u0634\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u062f\u0642\u06cc\u0642 \u0622\u06af\u0627\u0647<\/strong>: \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0647 \u0627\u0644\u0632\u0627\u0645\u0627\u062a \u062f\u0642\u06cc\u0642 \u062d\u0633\u0627\u0633 \u0647\u0633\u062a\u0646\u062f \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0642\u0627\u0628\u0644\u06cc\u062a \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0631\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u062f\u0647\u062f.<\/p>\n<\/li>\n<\/ul>\n<h2>\u0645\u0634\u062e\u0635\u0627\u062a \u0627\u0635\u0644\u06cc \u0648 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627 \u0627\u0635\u0637\u0644\u0627\u062d\u0627\u062a \u0645\u0634\u0627\u0628\u0647<\/h2>\n<p>\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0627\u063a\u0644\u0628 \u0628\u0627 \u062f\u06cc\u06af\u0631 \u0646\u0645\u0627\u06cc\u0634 \u0647\u0627\u06cc \u0639\u062f\u062f\u06cc 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\u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc<\/strong>: \u0631\u0627\u06cc\u0627\u0646\u0647 \u0647\u0627\u06cc \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u062a\u06a9\u0646\u06cc\u06a9 \u0647\u0627\u06cc \u062c\u062f\u06cc\u062f\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0639\u062f\u062f\u06cc \u0645\u0639\u0631\u0641\u06cc \u06a9\u0646\u0646\u062f \u06a9\u0647 \u0628\u0647 \u0637\u0648\u0631 \u0628\u0627\u0644\u0642\u0648\u0647 \u0628\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u062a\u0623\u062b\u06cc\u0631 \u0645\u06cc \u06af\u0630\u0627\u0631\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u0641\u0631\u0627\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646<\/strong>: \u0628\u0631\u0646\u0627\u0645\u0647 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f\u06cc \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0648 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0627\u0639\u062b \u067e\u06cc\u0634\u0631\u0641\u062a \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0639\u062f\u062f\u06cc \u0628\u0631\u0627\u06cc \u062a\u0637\u0628\u06cc\u0642 \u0645\u062f\u0644 \u0647\u0627 \u0648 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0634\u0648\u062f.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0686\u06af\u0648\u0646\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0633\u0631\u0648\u0631\u0647\u0627\u06cc \u067e\u0631\u0627\u06a9\u0633\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f \u06cc\u0627 \u0628\u0627 \u062d\u0633\u0627\u0628 \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0645\u0631\u062a\u0628\u0637 \u0634\u062f<\/h2>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0633\u0631\u0648\u0631\u0647\u0627\u06cc \u067e\u0631\u0648\u06a9\u0633\u06cc \u062f\u0631 \u062f\u0631\u062c\u0647 \u0627\u0648\u0644 \u0628\u0631 \u062a\u0633\u0647\u06cc\u0644 \u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u0634\u0628\u06a9\u0647 \u062a\u0645\u0631\u06a9\u0632 \u0645\u06cc \u06a9\u0646\u0646\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0647 \u0637\u0648\u0631 \u063a\u06cc\u0631\u0645\u0633\u062a\u0642\u06cc\u0645 \u0628\u0627 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u062f\u0631 \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0628\u0627\u062f\u0644\u0647 \u0634\u062f\u0647 \u0634\u0627\u0645\u0644 \u0627\u0639\u062f\u0627\u062f \u0648\u0627\u0642\u0639\u06cc \u0647\u0633\u062a\u0646\u062f \u0645\u0631\u062a\u0628\u0637 \u0634\u0648\u0646\u062f. \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0633\u0631\u0648\u0631\u0647\u0627\u06cc \u067e\u0631\u0627\u06a9\u0633\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u062f\u0631 \u0627\u0646\u062a\u0642\u0627\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc\u060c \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0645\u0627\u0644\u06cc \u06cc\u0627 \u0641\u0627\u06cc\u0644 \u0647\u0627\u06cc \u0631\u0633\u0627\u0646\u0647 \u0627\u06cc \u0646\u0642\u0634 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f \u06a9\u0647 \u0647\u0645\u06af\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u062d\u0627\u0648\u06cc \u0627\u0639\u062f\u0627\u062f \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0627\u0634\u0646\u062f. \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0627\u0632 \u0635\u062d\u062a \u0648 \u062f\u0642\u062a \u0627\u06cc\u0646 \u0627\u0639\u062f\u0627\u062f \u062f\u0631 \u062d\u06cc\u0646 \u0627\u0646\u062a\u0642\u0627\u0644 \u0627\u0645\u0631\u06cc \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a \u0648 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0635\u062d\u06cc\u062d \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0628\u0631\u0627\u06cc \u062d\u0641\u0638 \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627 \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a.<\/p>\n<h2>\u0644\u06cc\u0646\u06a9 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647<\/h2>\n<p>\u0628\u0631\u0627\u06cc \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u0645\u0646\u0627\u0628\u0639 \u0632\u06cc\u0631 \u0645\u0631\u0627\u062c\u0639\u0647 \u06a9\u0646\u06cc\u062f:<\/p>\n<ul>\n<li><a href=\"https:\/\/standards.ieee.org\/standard\/754-2019.html\" target=\"_new\" rel=\"noopener nofollow\">\u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f IEEE 754<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Floating-point_arithmetic\" target=\"_new\" rel=\"noopener nofollow\">\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631 \u062f\u0631 \u0648\u06cc\u06a9\u06cc \u067e\u062f\u06cc\u0627<\/a><\/li>\n<li><a href=\"https:\/\/docs.oracle.com\/cd\/E19957-01\/806-3568\/ncg_goldberg.html\" target=\"_new\" rel=\"noopener nofollow\">\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0639\u062f\u062f\u06cc \u0628\u0627 \u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u0645\u0645\u06cc\u0632 \u0634\u0646\u0627\u0648\u0631<\/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\/ir\/wp-json\/wp\/v2\/wiki\/477261","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki\/477261\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/media\/468423"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/media?parent=477261"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}