{"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":145,"pdf_page":161,"physical_index":161,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"eedfa98916bf9bae96c2855da0e4a898b68fde552d132da067642f2783ce94ee"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"这就是表示多位数字中各位数字的常用方法。 $\\mathbf { A } _ { 0 }$ 、 $\\mathrm { B } _ { 0 }$ 和 ${ \\bf S } _ { 0 }$ 是最低有效位，或者说是最右边的一位。 $\\mathbf { A } _ { 7 }$ 、 $\\mathbf { B } _ { 7 }$ 和 $\\mathbf { S } _ { 7 }$ 是最高有效位，或者说是最左边的一位。例如，下面演示了这样一列带有下标的字母是如何用来表示一个二进制数0110-1001的。\n\n$$\n\\begin{array} { r c c c c c c c c c } { \\mathsf { A } _ { \\gamma } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } & { \\mathsf { A } _ { \\varepsilon } } \\\\ { 0 } & { \\uparrow } & { \\uparrow } & { 0 } & { \\uparrow } & { 0 } & { 0 } & { 1 } \\end{array}\n$$\n\n下标从0开始，并且向着高有效位的方向递增，因为它们和2的乘方数（幂）相对应。\n\n$$\n\\begin{array} { c c c c c c c c c } { { 2 ^ { 7 } } } & { { 2 ^ {  } } } & { { 2 ^ {  } } } & { { 2 ^ {  } } } & { { 2 ^ {  } } } & { { 2 ^ {  } } } & { { 2 ^ { z } } } & { { 2 ^ {  } } } & { { 2 ^ {  } } } & { { } } \\\\ { { 0 } } & { { 1 } } & { { 1 } } & { { 0 } } & { { 1 } } & { { 0 } } & { { 0 } } & { { 1 } } \\end{array}\n$$\n\n如果把下面一排的每个二进制位和其对应的2的幂相乘再依次相加，你就会得到0110-1001的十进制数表示 $6 4 + 3 2 + 8 + 1$ ，即105。\n\n另一种8位二进制加法器可用下图表示。\n\n双线箭头包含了8个输入端，代表一组8个独立的信号。它们被标识为 $\\mathbf { A } _ { 7 } . . . \\mathbf { A } _ { 0 } , \\ \\mathbf { B } _ { 7 } . . . \\mathbf { B } _ { 0 }$ $\\mathbf { S } _ { 7 } . . . \\mathbf { S } _ { 0 }$ ，同样也表示一个8位二进制数。\n\n一旦你搭建起了8位二进制加法器，你就可以再搭建另外一个加法器。把它们级联起来就可以很容易地扩展出一个16位加法器。\n\n12 二进制加法器\n\n145","previous_page":144,"next_page":146}