{"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":67,"pdf_page":83,"physical_index":83,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"f76cb3913fa0db98e1d1a5e02e4c099850fe3a89a45ef5dbb4b74e3ef7201970"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"运算要简单些。这将是你真正喜欢二进制数的地方。想象一下，如果你记住了如下表格，掌握加法将是一件多么迅速的事情啊。\n\n让我们用这个表格来计算两个二进制数的和：\n\n$$\n\\frac { 1 1 0 0 1 0 1 } { 1 0 0 1 1 0 1 1 }\n$$\n\n从最右一列开始：1加0等于 $\\mathbf { l } _ { \\mathrm { ~ o ~ } }$ 右边第二列：0加1等于 $1 _ { \\circ }$ 第三列：1加1等于0，进 $1 _ { \\circ }$ 第四列：1（进位）加0加0等于 $1 _ { \\circ }$ 第五列：0加1等于 $1 _ { \\circ }$ 第六列：1加1等于0，进1。第七列：1（进位）加1加0等于10。\n\n乘法表甚至比加法表还要简单，因为该表可以由两个基本的乘法规则推导出来：任何数乘以0结果都为0，任何数乘以1，结果都是这个数本身。\n\n以下是 $1 3 _ { \\mathrm { T E N } }$ 与 $1 1 _ { \\mathsf { T E N } }$ 的二进制乘法运算过程：\n\n$$\n\\begin{array} { r } { 1 1 0 1 } \\\\ { \\frac { \\times 1 0 1 1 } { 1 1 0 1 } } \\\\ { 1 1 0 1 } \\\\ { 0 0 0 0 } \\\\ { \\frac { 1 1 0 1 1 } { 1 0 0 1 1 1 1 } } \\end{array}\n$$\n\n结果为 $1 4 3 _ { \\mathrm { ~ T E N } }$ 0\n\n人们在使用二进制数的时候通常将它们写成带有前导零的形式（即第一个1的左边有零)。例如0011，而不是写做11。这样写不会改变数字的大小，仅仅是为了美观。例如，以下是前16个二进制数以及与它们等价的十进制数。\n\n8 十的替代品\n\n67","previous_page":66,"next_page":68}