{"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":92,"pdf_page":108,"physical_index":108,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"f487d16ba9aad202fa9d16fd0c20438cf076b02ee5976ebe2de4456811a0bbe5"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"布尔发明了一种代数，这种代数看上去与传统代数非常相似，而且运算规则也非常类似。在传统的代数中，操作数（通常为字母）代表数字，算子（通常为“+”和“×”）则用来指示这些数字之间如何运算。通常，我们应用传统代数来解决可能像这样的问题：安雅有3磅豆腐。贝蒂的豆腐是安雅的2倍。卡门的豆腐比贝蒂多5磅。迪尔得丽的豆腐是卡门的3倍。试问迪尔得丽有多少豆腐？\n\n在解决这个问题时，我们首先要将文字叙述转化为数学语言，下面用四个字母分别表示每个人所拥有的豆腐有多少磅：\n\n$$\n\\begin{array} { l } { A = 3 } \\\\ { B = 2 \\times A } \\\\ { C = B + 5 } \\\\ { D = 3 \\times C } \\end{array}\n$$\n\n将以上4个表达式带入同一式子中合并，最终可以得到一个加法和乘法混合运算的式子：\n\n$$\n\\begin{array} { l } { D = 3 \\times C } \\\\ { D = 3 \\times ( B + 5 ) } \\\\ { D = 3 \\times ( ( 2 \\times A ) + 5 ) } \\\\ { D = 3 \\times ( ( 2 \\times 3 ) + 5 ) } \\\\ { D = 3 3 } \\end{array}\n$$\n\n当进行传统代数运算的时候，我们会遵循一定的规则。这些规则在实际中可能非常根深蒂固，以至于我们不再认为它们是规则，甚至可能忘记它们的名字。但规则确实是任何形式数学运算的基础。\n\n首先是加法和乘法的交换律(commutative)。意思就是，在运算符两边的操作数可以任意调换：\n\n$$\n\\begin{array} { l } { { A + B = B + A } } \\\\ { { \\ } } \\\\ { { A \\times B = B \\times A } } \\end{array}\n$$\n\n相反，减法和除法则是无法应用交换律的。\n\n编码——隐匿在计算机软硬件背后的语言\n\n92","previous_page":91,"next_page":93}