{"id":3608,"date":"2026-03-20T11:06:18","date_gmt":"2026-03-20T11:06:18","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3608"},"modified":"2026-04-19T11:16:44","modified_gmt":"2026-04-19T11:16:44","slug":"binary-numbers","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/binary-numbers\/","title":{"rendered":"\u092c\u093e\u0907\u0928\u0930\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u2013 \u092a\u0939\u0932\u0940 \u092e\u0936\u0940\u0928 \u092d\u093e\u0937\u093e"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_ed88986f39805c81-493\" data-path-to-node=\"3\"><span data-path-to-node=\"3,0\"><b data-path-to-node=\"3,0\" data-index-in-node=\"0\">\u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/b> <\/span><span data-path-to-node=\"3,2\"><span class=\"citation-2468\">\u092c\u093e\u0907\u0928\u0930\u0940 \u092e\u0947\u0902 \u0915\u0947\u0935\u0932 \u0926\u094b \u0905\u0935\u0938\u094d\u0925\u093e\u090f\u0901 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902: \u0936\u0942\u0928\u094d\u092f (\u092c\u0902\u0926) \u0914\u0930 \u090f\u0915 (\u091a\u093e\u0932\u0942)\u0964<\/span><\/span><span data-path-to-node=\"3,4\">. <\/span><span data-path-to-node=\"3,6\"><span class=\"citation-2467\">\u092f\u0939 \u0935\u0939 &#039;\u092e\u0936\u0940\u0928 \u092d\u093e\u0937\u093e&#039; \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0906\u091c \u0938\u092d\u0940 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930, \u092e\u094b\u092c\u093e\u0907\u0932 \u092b\u094b\u0928 \u0914\u0930 \u0915\u0943\u0924\u094d\u0930\u093f\u092e \u092c\u0941\u0926\u094d\u0927\u093f\u092e\u0924\u094d\u0924\u093e \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u093e\u0901 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"3,8\">. <\/span><span data-path-to-node=\"3,10\"><span class=\"citation-2466\">\u092f\u0939 \u0938\u092d\u0940 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u094b \u0939\u093e\u0902\/\u0928\u093e \u0935\u093f\u0915\u0932\u094d\u092a\u094b\u0902 \u0915\u0940 \u090f\u0915 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"3,12\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-494\" data-path-to-node=\"4\"><span data-path-to-node=\"4,0\"><b data-path-to-node=\"4,0\" data-index-in-node=\"0\">\u0915\u0939\u093e\u0928\u0940<\/b> <\/span><span data-path-to-node=\"4,2\"><span class=\"citation-2465\">\u092a\u0939\u0932\u0947 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u091a\u093f\u092a \u0915\u0947 \u0906\u0935\u093f\u0937\u094d\u0915\u093e\u0930 \u0938\u0947 \u092c\u0939\u0941\u0924 \u092a\u0939\u0932\u0947, \u092a\u093f\u0902\u0917\u0932\u093e \u0928\u093e\u092e\u0915 \u090f\u0915 \u092d\u093e\u0930\u0924\u0940\u092f \u090b\u0937\u093f \u0915\u0935\u093f\u0924\u093e \u0915\u0940 \u0932\u092f \u0915\u0947 \u092a\u094d\u0930\u0924\u093f \u0906\u0938\u0915\u094d\u0924 \u0925\u0947\u0964<\/span><\/span><span data-path-to-node=\"4,4\">. <\/span><span data-path-to-node=\"4,6\"><span class=\"citation-2464\">\u0935\u0939 \u092c\u093f\u091c\u0932\u0940 \u0915\u0940 \u0924\u0932\u093e\u0936 \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0925\u093e; \u0935\u0939 \u0938\u0902\u0917\u0940\u0924 \u0915\u0947 \u0924\u0930\u094d\u0915 \u0915\u0940 \u0924\u0932\u093e\u0936 \u092e\u0947\u0902 \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"4,8\">. <\/span><span data-path-to-node=\"4,10\"><span class=\"citation-2463\">\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u093e\u0935\u094d\u092f \u091b\u0902\u0926 \u0915\u094b &#039;\u0932\u0918\u0941&#039; (0) \u0914\u0930 &#039;\u0926\u0940\u0930\u094d\u0918&#039; (1) \u0936\u092c\u094d\u0926\u093e\u0902\u0936\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0915\u0947, \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u0940 \u092a\u0939\u0932\u0940 &#039;\u092e\u0936\u0940\u0928 \u092d\u093e\u0937\u093e&#039; \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u093f\u092f\u093e\u0964\u2018<\/span><\/span><span data-path-to-node=\"4,12\">. <\/span><span data-path-to-node=\"4,14\"><span class=\"citation-2462\">\u0939\u093e\u0932\u093e\u0902\u0915\u093f \u0907\u0924\u093f\u0939\u093e\u0938 \u0915\u0940 \u0915\u093f\u0924\u093e\u092c\u094b\u0902 \u092e\u0947\u0902 \u0905\u0915\u094d\u0938\u0930 \u0932\u093e\u0907\u092c\u0928\u093f\u091c\u093c \u0915\u094b 1600 \u0915\u0947 \u0926\u0936\u0915 \u092e\u0947\u0902 \u092c\u093e\u0907\u0928\u0930\u0940 \u0915\u093e \u0906\u0935\u093f\u0937\u094d\u0915\u093e\u0930\u0915 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u092a\u093f\u0902\u0917\u0932\u093e \u0915\u0947 \u091b\u0902\u0926 \u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u092e\u0947\u0902 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 \u0926\u094b\u0917\u0941\u0928\u0947 \u0914\u0930 \u0906\u0927\u0947 \u0915\u0930\u0928\u0947 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e \u091c\u094b \u0906\u091c \u0906\u092a\u0915\u0947 \u0938\u094d\u092e\u093e\u0930\u094d\u091f\u092b\u094b\u0928 \u0915\u094b \u091a\u0932\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"4,16\">. <\/span><span data-path-to-node=\"4,18\"><span class=\"citation-2461\">\u092f\u0939 \u090f\u0915 \u0905\u0924\u094d\u092f\u0902\u0924 \u0935\u093f\u0921\u0902\u092c\u0928\u093e \u0939\u0948: \u0915\u0943\u0924\u094d\u0930\u093f\u092e \u092c\u0941\u0926\u094d\u0927\u093f\u092e\u0924\u094d\u0924\u093e \u0915\u093e \u0915\u094b\u0921 \u0938\u0930\u094d\u0935\u092a\u094d\u0930\u0925\u092e \u092a\u094d\u0930\u093e\u091a\u0940\u0928 \u0936\u094d\u0932\u094b\u0915\u094b\u0902 \u0915\u0947 \u0909\u091a\u094d\u091a\u093e\u0930\u0923 \u0915\u094b \u092a\u0930\u093f\u092a\u0942\u0930\u094d\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0932\u093f\u0916\u093e \u0917\u092f\u093e \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"4,20\">.<\/span><\/p>\n<p data-path-to-node=\"5\"><b data-path-to-node=\"5\" data-index-in-node=\"0\">\u0938\u092e\u092f\u0930\u0947\u0916\u093e<\/b><\/p>\n<table data-path-to-node=\"6\">\n<thead>\n<tr>\n<td><strong>\u092e\u0940\u0932 \u0915\u093e \u092a\u0924\u094d\u0925\u0930<\/strong><\/td>\n<td><strong>\u0935\u093f\u0935\u0930\u0923<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"6,1,0,0\"><b data-path-to-node=\"6,1,0,0\" data-index-in-node=\"0\">\u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0938\u0902\u0926\u0930\u094d\u092d.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-495\" data-path-to-node=\"6,1,1,0\"><span data-path-to-node=\"6,1,1,0,1\"><span class=\"citation-2460\">1679 \u0908\u0938\u094d\u0935\u0940 (\u0917\u0949\u091f\u092b\u094d\u0930\u0940\u0921 \u0935\u093f\u0932\u094d\u0939\u0947\u092e \u0932\u093e\u0907\u092c\u0928\u093f\u091c\u093c)<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"6,2,0,0\"><b data-path-to-node=\"6,2,0,0\" data-index-in-node=\"0\">\u092d\u093e\u0930\u0924\u0940\u092f \u0938\u094d\u0930\u094b\u0924<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-496\" data-path-to-node=\"6,2,1,0\"><span data-path-to-node=\"6,2,1,0,1\"><span class=\"citation-2459\">2,000 \u0908\u0938\u093e \u092a\u0942\u0930\u094d\u0935 \u0938\u0947 \u092a\u0939\u0932\u0947 (\u092a\u093f\u0902\u0917\u0932\u093e \u0915\u093e \u091b\u0902\u0926 \u0936\u093e\u0938\u094d\u0924\u094d\u0930)<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"6,3,0,0\"><b data-path-to-node=\"6,3,0,0\" data-index-in-node=\"0\">\u0915\u093e\u0932 \u0905\u0902\u0924\u0930\u093e\u0932<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-497\" data-path-to-node=\"6,3,1,0\"><span data-path-to-node=\"6,3,1,0,1\"><span class=\"citation-2458\">3,500 \u0935\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u092d\u0940 \u0905\u0927\u093f\u0915<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-path-to-node=\"7\"><b data-path-to-node=\"7\" data-index-in-node=\"0\">\u0938\u092c\u0942\u0924<\/b><\/p>\n<blockquote data-path-to-node=\"8\">\n<p id=\"p-rc_ed88986f39805c81-498\" data-path-to-node=\"8,1\"><span data-path-to-node=\"8,1,0\"><b data-path-to-node=\"8,1,0\" data-index-in-node=\"0\"><span class=\"citation-2457\">\u0938\u0902\u0938\u094d\u0915\u0943\u0924 \u0936\u094d\u0932\u094b\u0915:<\/span><\/b><span class=\"citation-2457\"> \u0926\u094d\u0935\u093f\u0930\u0930\u094d\u0927\u0947 \u0924\u0926\u0928\u094d\u0924\u093e\u0928\u093e\u092e\u094d \u0917\u094d\u0932\u094c \u0907\u0924\u093f\u0964 <\/span><\/span><span data-path-to-node=\"8,1,3\"><b data-path-to-node=\"8,1,3\" data-index-in-node=\"0\"><span class=\"citation-2456\">\u0932\u093f\u092a\u094d\u092f\u0902\u0924\u0930\u0923:<\/span><\/b><span class=\"citation-2456\"> \u0926\u0935\u093f\u0930 \u0905\u0930\u094d\u0927\u0947 \u0924\u0926\u094d \u0905\u0928\u094d\u0924\u094d\u092f\u0928\u093e\u092e \u0917\u094d\u0932\u094c \u0907\u0924\u093f\u0964. <\/span><\/span><span data-path-to-node=\"8,1,5\"> <b data-path-to-node=\"8,1,5\" data-index-in-node=\"1\">\u0905\u0930\u094d\u0925:<\/b> \u2018\u091c\u092c \u0938\u0902\u0916\u094d\u092f\u093e \u0906\u0927\u0940 \u0939\u094b (\u0926\u094b \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u094b), \u0924\u094b \u0917\u0941\u0930\u0941 (\u092d\u093e\u0930\u0940 \u0905\u0915\u094d\u0937\u0930\/1) \u0932\u093f\u0916\u0947\u0902; \u091c\u092c \u0935\u0939 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0928 \u0939\u094b, \u0924\u094b \u090f\u0915 \u0918\u091f\u093e\u090f\u0901 \u0914\u0930 \u0932\u0918\u0941 (\u0939\u0932\u094d\u0915\u093e \u0905\u0915\u094d\u0937\u0930\/0) \u0932\u093f\u0916\u0947\u0902\u0964 (\u092f\u0939\u0940 1 \u0914\u0930 0 \u0915\u093e \u092e\u0942\u0932 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0939\u0948)\u0964 (\u092a\u093f\u0902\u0917\u0932\u093e \u091b\u0902\u0926 \u0938\u0942\u0924\u094d\u0930 8.23) <\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/blockquote>\n<p id=\"p-rc_ed88986f39805c81-499\" data-path-to-node=\"9\"><span data-path-to-node=\"9,0\"><b data-path-to-node=\"9,0\" data-index-in-node=\"0\">\u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u0935\u093e\u091a\u093e\u0930<\/b> <\/span><span data-path-to-node=\"9,2\"><span class=\"citation-2454\">\u0915\u093e\u091f\u093e\u092a\u092f\u093e\u0926\u093f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0938\u0902\u0917\u0940\u0924 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0915\u0930\u0924\u0940 \u0925\u0940, \u0914\u0930 \u0935\u0948\u0926\u093f\u0915 \u092e\u0902\u0924\u094d\u0930\u094b\u091a\u094d\u091a\u093e\u0930 \u092e\u0947\u0902 \u0924\u094d\u0930\u0941\u091f\u093f\u092f\u094b\u0902 \u0915\u094b \u0926\u0942\u0930 \u0915\u0930\u0928\u0947 \u0914\u0930 \u0905\u0915\u094d\u0937\u0930\u094b\u0902 \u0915\u0947 \u0938\u0939\u0940 \u0909\u091a\u094d\u091a\u093e\u0930\u0923 \u0915\u094b \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u093e\u0907\u0928\u0930\u0940 \u0915\u094b\u0921 \u091c\u0948\u0938\u0947 \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"9,4\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-500\" data-path-to-node=\"10\"><span data-path-to-node=\"10,0\"><b data-path-to-node=\"10,0\" data-index-in-node=\"0\">\u092e\u091c\u0947\u0926\u093e\u0930 \u0924\u0925\u094d\u092f<\/b> <\/span><span data-path-to-node=\"10,2\"><span class=\"citation-2453\">\u092a\u093f\u0902\u0917\u0932\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093e\u0935\u094d\u092f \u0938\u0902\u092f\u094b\u091c\u0928\u094b\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u093f\u090f \u0917\u090f \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0906\u092a\u0915\u0947 \u0932\u0948\u092a\u091f\u0949\u092a \u0915\u094b \u0938\u0902\u091a\u093e\u0932\u093f\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u0915\u094b\u0921 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"10,4\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-501\" data-path-to-node=\"11\"><span data-path-to-node=\"11,0\"><b data-path-to-node=\"11,0\" data-index-in-node=\"0\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0930\u093e\u0938\u0924<\/b> <\/span><span data-path-to-node=\"11,2\"><span class=\"citation-2452\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u0940 &#039;\u092e\u0936\u0940\u0928 \u092d\u093e\u0937\u093e&#039; \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u092f\u0939 \u0924\u0930\u094d\u0915 \u0938\u0902\u092a\u0942\u0930\u094d\u0923 \u0938\u0942\u091a\u0928\u093e \u092f\u0941\u0917 \u0915\u093e \u0906\u0927\u093e\u0930 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"11,4\">. <\/span><span data-path-to-node=\"11,6\"><span class=\"citation-2451\">\u092a\u093f\u0902\u0917\u0932\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u0930\u094d\u0935\u092a\u094d\u0930\u0925\u092e \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u093f\u0924 \u092c\u093e\u0907\u0928\u0930\u0940 \u092b\u094d\u0930\u0947\u092e\u0935\u0930\u094d\u0915 \u0915\u0947 \u092c\u093f\u0928\u093e \u0921\u093f\u091c\u093f\u091f\u0932 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u093f\u0902\u0917 \u0905\u0938\u0902\u092d\u0935 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"11,8\">.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3497,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[399,544,551,552,554,553,542],"class_list":["post-3608","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-algorithms","tag-ancient-indian-mathematics","tag-binary-numbers","tag-chandas-shastra","tag-computer-science-roots","tag-machine-language","tag-pingala"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\r\n<title>Binary Numbers \u2013 The First Machine Language - BharatWisdom<\/title>\r\n<meta name=\"description\" content=\"Excerpt\" \/>\r\n<meta name=\"robots\" content=\"index, follow, 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