{"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":134,"pdf_page":150,"physical_index":150,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"cfade633778ad06bcb04783bb30f78211541f9ff77e330d8e4db3fcf9f5f912e"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"只有当输入全为1时，输出才为0。\n\n这两组等价关系就是摩根定律在电路中的实现。摩根是维多利亚女王时代的另一位数学家，比布尔大9岁，于1847年发表《形式逻辑》(FormalLogic)一书，与布尔的《逻辑的数学分析》(The Mathematical Analysis ofLogic)恰好同一天出版（据说是同一天)。实际上，布尔研究逻辑的灵感正源于一场公开的争论，这个争论就发生在摩根和另一个被指剽窃的英国数学家之间（历史最后证实摩根是清白的）。摩根很早就发现了布尔的洞察力。他无私地鼓励布尔，并帮助他开展研究，而今天除了他的这个著名定律之外，他几乎已被人们所遗忘。\n\n摩根定律可以简单地表示为如下形式：\n\n$$\n{ \\begin{array} { r } { { \\overline { { \\mathbf { A } } } } \\times { \\overline { { \\mathbf { B } } } } = { \\overline { { \\mathbf { A } + \\mathbf { B } } } } } \\\\ { { \\overline { { \\mathbf { A } } } } + { \\overline { { \\mathbf { B } } } } = { \\overline { { \\mathbf { A } \\times \\mathbf { B } } } } } \\end{array} }\n$$\n\nA和B是两个布尔操作数。在第一个表达式中，两个操作数先被取反，再进行与运算。这与两个操作数进行或运算后再取反（即或非）的结果是一样的。在第二个表达式中，两个操作数先取反，再进行或运算，这和两个操作数先做与运算后再取反（即与非）的结果是等价的。\n\n摩根定律是简化布尔表达式的一种重要手段，因此也可以用来简化电路。从历史的角度来说，这正是香农的论文带给电气工程师们的真正意义。但在本书中简化电路不是重点，我们关注的是让一切有效地运转而不是以最简的形式运转。我们下面要做的就是一台加法器。\n\n编码隐匿在计算机软硬件背后的语言\n\n134","previous_page":133,"next_page":null}