{"resolved":true,"match_type":"uuid","source_type":"original_book","book_id":"38270854-596f-4a26-8183-db8c968c6020","title":"编码 隐匿在计算机软硬件背后的语言","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787121181184","requested_by":"printed_page","book":{"source_type":"original_book","book_id":"38270854-596f-4a26-8183-db8c968c6020","id":"38270854-596f-4a26-8183-db8c968c6020","uuid":"38270854-596f-4a26-8183-db8c968c6020","title":"编码 隐匿在计算机软硬件背后的语言","normalized_title":"编码隐匿在计算机软硬件背后的语言","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787121181184","isbns":["9787121181184","0123456789","6044921875","3039331000","0000000000","0000000000000"],"parsed":true,"ai_readable":true,"document_type":"book","page_count":438,"navigation_url":"https://workshop.closeclaw.top/ai/book/38270854-596f-4a26-8183-db8c968c6020","title_url":"https://workshop.closeclaw.top/ai/title/%E7%BC%96%E7%A0%81%20%E9%9A%90%E5%8C%BF%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E8%BD%AF%E7%A1%AC%E4%BB%B6%E8%83%8C%E5%90%8E%E7%9A%84%E8%AF%AD%E8%A8%80","fixed_page_url_template":"https://workshop.closeclaw.top/ai/book/38270854-596f-4a26-8183-db8c968c6020/page/{printed_page}","path_api_url_template":"https://workshop.closeclaw.top/api/ai/book/38270854-596f-4a26-8183-db8c968c6020/page/{printed_page}","read_url":"https://workshop.closeclaw.top/api/ai/read/38270854-596f-4a26-8183-db8c968c6020","page_url":"https://workshop.closeclaw.top/api/ai/books/38270854-596f-4a26-8183-db8c968c6020/page","search_url":"https://workshop.closeclaw.top/api/ai/books/38270854-596f-4a26-8183-db8c968c6020/search"},"page":{"printed_page":3754,"pdf_page":391,"physical_index":391,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"efde8faa97ee79716f8a2f6ccbf7dfe52585f2425ca9b4d7318320b365978d14"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"单精度浮点数的有效表示范围。\n\n如前所述，10位二进制数可以近似地用3位十进制数来表示。其含义是，如果把10位都置为1，即十六进制的3FFh或十进制的1023，它近似等于把十进制数的3位都置为9，即999，可以表示为下面的约等式：\n\n$$\n2 ^ { 1 0 } \\approx 1 0 ^ { 3 }\n$$\n\n两者之间的这种关系意味着：单精度浮点数格式存放的24位二进制数大体上与7位的十进制数相等。因此，可以说单精度浮点格式提供24位的二进制精度或者7位的十进制精度。其深层的含义是什么呢？\n\n当我们查看定点数时，其精确度是很明显的。例如，当我们表示钱款时，采用两位定点小数就可以精确到美分。但是对于采用浮点格式的数，就不能如此肯定了。其精确度依赖于指数的值，有时候浮点数可以精确到比美分还小的单位，但有时候其精确度甚至达不到美元。\n\n这样说可能更合适：单精度浮点数的精度为 $1 / 2 ^ { 2 4 }$ ，或1/16777216，或百万分之六，但其真正的含义是什么呢？\n\n首先，这意味着在单精度浮点格式下，16,777,216和16,777,217将表示成同一个数。不仅如此，处于这两个数之间的所有的数（例如，16,777,216.5）也将被表示成同一个数。所以上面提到的3个十进制数都按32位单精度浮点数：\n\n4B800000h\n\n来存放。将该数按符号位、指数位和有效数位划分，可以表示为：\n\n$$\n0 \\ 1 0 0 1 0 1 1 1 \\ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n$$\n\n也就是：\n\n$$\n1 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _ { 2 } \\times 2 ^ { 2 4 }\n$$\n\n下一个二进制浮点数可表示的最大有效数是16,777,218，即：\n\n$$\n1 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 _ { 2 } \\times 2 ^ { 2 4 }\n$$\n\n23 定点数和浮点数\n\n3754","previous_page":null,"next_page":null}