{"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":62,"pdf_page":78,"physical_index":78,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"656d6abd0c86fb77d2dee89a594ff4b93597ec2228465f73f9e33e9c8eb34957"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"四进制数字系统是像这样计数的：0，1，2，3，10，11，12，13，20，21，22，23，30，31，32，33，100，101，102，103，110，等等。\n\n这里我不打算在四进制数上花太多的时间，因为接下来我们即将转入一个更为重要的话题。通过下图我们可以看出四进制中每一位是如何跟4的某个整数次幂相对应的。\n\n四进制数31232可以写做如下形式：\n\n$$\n\\begin{array} { r l r } { 3 1 2 3 2 _ { \\mathrm { F O U R } } = 3 \\times 2 5 6 _ { \\mathrm { T E N } } + } & { } & \\\\ { \\phantom { \\frac { 1 } { 2 } } } & { 1 \\times 6 4 _ { \\mathrm { T E N } } + } & { } \\\\ { \\phantom { \\frac { 1 } { 2 } } } & { 2 \\times 1 6 _ { \\mathrm { T E N } } + } & { } \\\\ { \\phantom { \\frac { 1 } { 2 } } } & { 3 \\times 4 _ { \\mathrm { T E N } } + } & { } \\\\ { \\phantom { \\frac { 1 } { 2 } } } & { 2 \\times 1 } & { } \\end{array}\n$$\n\n等价于：\n\n$$\n\\begin{array} { c } { { 3 1 2 3 2 _ { \\mathrm { F O U R } } = 3 \\times 1 0 0 0 0 _ { \\mathrm { F O U R } } + } } \\\\ { { } } \\\\ { { 1 \\times 1 0 0 0 _ { \\mathrm { F O U R } } + } } \\\\ { { } } \\\\ { { 2 \\times 1 0 0 _ { \\mathrm { F O U R } } + } } \\\\ { { } } \\\\ { { 3 \\times 1 0 _ { \\mathrm { F O U R } } + } } \\\\ { { } } \\\\ { { 2 \\times 1 } } \\end{array}\n$$\n\n同样可以写成：\n\n$$\n\\begin{array} { r } { 3 1 2 3 2 _ { \\mathrm { F O U R } } = 3 \\times 4 ^ { 4 } + } \\\\ { 1 \\times 4 ^ { 3 } + } \\\\ { 2 \\times 4 ^ { 2 } + } \\\\ { 3 \\times 4 ^ { 1 } + } \\\\ { 2 \\times 4 ^ { 0 } } \\end{array}\n$$\n\n编码—隐匿在计算机软硬件背后的语言\n\n62","previous_page":61,"next_page":63}