{"id":399,"date":"2026-05-13T19:14:05","date_gmt":"2026-05-13T19:14:05","guid":{"rendered":"https:\/\/edk-tech.net\/?p=399"},"modified":"2026-05-13T19:14:07","modified_gmt":"2026-05-13T19:14:07","slug":"converting-number-systems","status":"publish","type":"post","link":"https:\/\/edk-tech.net\/?p=399","title":{"rendered":"Converting Number Systems"},"content":{"rendered":"\n
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IPv4<\/a> addresses 2<\/mn>32<\/mn><\/msup>=<\/mo>4,294,967,296<\/mn><\/mrow>2^{32}=4,294,967,296<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

n 2<\/mn>7<\/mn><\/msup>2<\/mn>6<\/mn><\/msup>2<\/mn>5<\/mn><\/msup>2<\/mn>4<\/mn><\/msup>2<\/mn>3<\/mn><\/msup>2<\/mn>2<\/mn><\/msup>2<\/mn>1<\/mn><\/msup>2<\/mn>0<\/mn><\/msup><\/mrow>2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

Assignable IP addresses 2<\/mn>h<\/mi><\/msup>\u2212<\/mo>2<\/mn><\/mrow>2^h-2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

Subnets 2<\/mn>s<\/mi><\/msup>2^s<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

block size 256<\/mn>\u2212<\/mo>I<\/mi>n<\/mi>t<\/mi>e<\/mi>r<\/mi>e<\/mi>s<\/mi>t<\/mi>i<\/mi>n<\/mi>g<\/mi>O<\/mi>c<\/mi>t<\/mi>e<\/mi>t<\/mi><\/mrow>256-Interesting Octet<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    \n
  1. 2748<\/mn>\u00f7<\/mo>16<\/mn>=<\/mo>171<\/mn><\/mrow>2748 \\div 16 = 171<\/annotation><\/semantics><\/math> with a remainder of 12<\/mn>12<\/annotation><\/semantics><\/math>; the hexadecimal value for 12<\/mn>12<\/annotation><\/semantics><\/math> is C<\/mi>C<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  2. 171<\/mn>\u00f7<\/mo>16<\/mn>=<\/mo>10<\/mn><\/mrow>171 \\div 16=10<\/annotation><\/semantics><\/math> with a remainder of 11<\/mn>11<\/annotation><\/semantics><\/math>; the hexadecimal value for 11<\/mn>11<\/annotation><\/semantics><\/math> is B<\/mi>B<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  3. 10<\/mn>\u00f7<\/mo>16<\/mn>=<\/mo>0<\/mn><\/mrow>10 \\div 16=0<\/annotation><\/semantics><\/math> with a remainder of 10; the hexadecimal value for 10<\/mn>10<\/annotation><\/semantics><\/math> is A<\/mi>A<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  4. The decimal value 2748<\/mn>2748<\/annotation><\/semantics><\/math> in hexadecimal format is A<\/mi>B<\/mi>C<\/mi><\/mrow>ABC<\/annotation><\/semantics><\/math>.<\/li>\n<\/ol>\n\n\n\n

    248\u00f72=124 124\u00f72=62124<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>62<\/mn><\/mrow>124\u00f72=62<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

    \"\begin{equation}<\/p>\n\n\n\n

    1: 124<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>62<\/mn><\/mrow><\/mo><\/mtd><\/mtr>124<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>62<\/mn><\/mrow><\/mo><\/mtd><\/mtr>62<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>31<\/mn><\/mrow><\/mo><\/mtd><\/mtr>31<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>15<\/mn><\/mrow><\/mo><\/mtd><\/mtr>15<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>7<\/mn><\/mrow><\/mo><\/mtd><\/mtr>7<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>3<\/mn><\/mrow><\/mo><\/mtd><\/mtr>3<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>1<\/mn><\/mrow><\/mo><\/mtd><\/mtr>1<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>0<\/mn><\/mrow><\/mtd><\/mtr><\/mtable>124\u00f72 =62\\\\ 124\u00f72=62\\\\ 62\u00f72=31\\\\ 31\u00f72=15\\\\ 15\u00f72=7\\\\ 7\u00f72=3\\\\ 3\u00f72=1\\\\ 1\u00f72=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    <\/mtd>124<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>62<\/mn><\/mrow><\/mtd><\/mtr>124<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>62<\/mn><\/mrow><\/mtd><\/mtr>62<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>31<\/mn><\/mrow><\/mtd><\/mtr>31<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>15<\/mn><\/mrow><\/mtd><\/mtr>15<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>7<\/mn><\/mrow><\/mtd><\/mtr>7<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>3<\/mn><\/mrow><\/mtd><\/mtr>3<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>1<\/mn><\/mrow><\/mtd><\/mtr>1<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>0<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><\/mtd><\/span><\/mtext><\/mtd><\/mtr><\/mtable>\\begin{equation}\n\\begin{split}\n124\u00f72 =62\\\\ 124\u00f72=62\\\\ 62\u00f72=31\\\\ 31\u00f72=15\\\\ 15\u00f72=7\\\\ 7\u00f72=3\\\\ 3\u00f72=1\\\\ 1\u00f72=0\n\\end{split}\n\\end{equation}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n\n248<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>124<\/mn><\/mrow>248\u00f72=124<\/annotation><\/semantics><\/math>\n\n\n\n124<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>62<\/mn><\/mrow>124\u00f72=62<\/annotation><\/semantics><\/math>\n\n\n\n62<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>31<\/mn><\/mrow>62\u00f72=31<\/annotation><\/semantics><\/math>\n\n\n\n31<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>15<\/mn><\/mrow>31\u00f72=15<\/annotation><\/semantics><\/math>\n\n\n\n15<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>7<\/mn><\/mrow>15\u00f72=7<\/annotation><\/semantics><\/math>\n\n\n\n7<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>3<\/mn><\/mrow>7\u00f72=3<\/annotation><\/semantics><\/math>\n\n\n\n3<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>1<\/mn><\/mrow>3\u00f72=1<\/annotation><\/semantics><\/math>\n\n\n\n1<\/mn>\u00f7<\/mo>2<\/mn>=<\/mo>0<\/mn><\/mrow>1\u00f72=0<\/annotation><\/semantics><\/math>\n\n\n\n\n
    3<\/mn>a<\/mi>x<\/mi>+<\/mo>4<\/mn>b<\/mi>y<\/mi>=<\/mo>5<\/mn>c<\/mi>z<\/mi><\/mrow><\/mtd><\/mtr>3<\/mn>a<\/mi>x<\/mi><<\/mo>4<\/mn>b<\/mi>y<\/mi>+<\/mo>5<\/mn>c<\/mi>z<\/mi><\/mrow><\/mtd><\/mtr><\/mtable>\\begin{align*}\n3ax+4by=5cz\\\\\n3ax<4by+5cz\\\\\n\\end{align*}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

    Total IPv6 2<\/mn>128<\/mn><\/msup>=<\/mo>3.4<\/mn>x<\/mi>10<\/mn>38<\/mn><\/msup><\/mrow>2^{128}=3.4×10^{38}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    <\/mtd><\/mrow>A<\/mi><\/mtd>=<\/mo>\u03c0<\/mi>r<\/mi>2<\/mn><\/msup><\/mrow>2<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mrow><\/mtd>=<\/mo>1<\/mn>2<\/mn><\/mfrac>\u03c0<\/mi>r<\/mi>2<\/mn><\/msup><\/mrow><\/mtd><\/mtr><\/mtable><\/mrow><\/mtd><\/span><\/mtext><\/mtd><\/mtr><\/mtable>\\begin{equation} \\label{eq1}\n\\begin{split}\nA & = \\frac{\\pi r^2}{2} \\\\\n & = \\frac{1}{2} \\pi r^2\n\\end{split}\n\\end{equation}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

    slope-intercept form: y<\/mi>=<\/mo>m<\/mi>x<\/mi>+<\/mo>b<\/mi><\/mrow>y=mx+b<\/annotation><\/semantics><\/math> ; <\/p>\n\n\n\n

    standard quadratic form: a<\/mi>x<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>x<\/mi>+<\/mo>c<\/mi>=<\/mo>0<\/mn><\/mrow>ax^2+bx+c=0<\/annotation><\/semantics><\/math> ; quadratic forumal: x<\/mi>=<\/mo>\u2212<\/mo>b<\/mi>\u00b1<\/mo>b<\/mi>2<\/mn><\/msup>\u2212<\/mo>4<\/mn>a<\/mi>c<\/mi><\/mrow><\/msqrt><\/mrow>2<\/mn>a<\/mi><\/mrow><\/mfrac><\/mrow>x=\\frac{-b \\pm \\sqrt{b^2-4ac}}{2a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

    speed: S<\/mi>=<\/mo>r<\/mi>t<\/mi><\/mrow>S=rt<\/annotation><\/semantics><\/math>; distance: time:<\/p>\n\n\n\n
    S<\/mi>p<\/mi>a<\/mi>c<\/mi>e<\/mi>s<\/mi>i<\/mi>n<\/mi>m<\/mi>a<\/mi>t<\/mi>h<\/mi>e<\/mi>m<\/mi>a<\/mi>t<\/mi>i<\/mi>c<\/mi>a<\/mi>l<\/mi>m<\/mi>o<\/mi>d<\/mi>e<\/mi>.<\/mi>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup><\/mspace>+<\/mo>3<\/mn>x<\/mi><\/mspace>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup>+<\/mo>3<\/mn>x<\/mi>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup><\/mspace>+<\/mo>3<\/mn>x<\/mi><\/mspace>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup><\/mspace>+<\/mo>3<\/mn>x<\/mi><\/mspace>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup><\/mspace>+<\/mo>3<\/mn>x<\/mi><\/mspace>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup> <\/mtext>+<\/mo>3<\/mn>x<\/mi> <\/mtext>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup><\/mspace>+<\/mo>3<\/mn>x<\/mi><\/mspace>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>2<\/mn><\/msup><\/mspace>+<\/mo>3<\/mn>x<\/mi><\/mspace>+<\/mo>2<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><\/mrow>Spaces in mathematical mode.\n\n\\begin{align*}\nf(x) &= x^2\\! +3x\\! +2 \\\\\nf(x) &= x^2+3x+2 \\\\\nf(x) &= x^2\\, +3x\\, +2 \\\\\nf(x) &= x^2\\: +3x\\: +2 \\\\\nf(x) &= x^2\\; +3x\\; +2 \\\\\nf(x) &= x^2\\ +3x\\ +2 \\\\\nf(x) &= x^2\\quad +3x\\quad +2 \\\\\nf(x) &= x^2\\qquad +3x\\qquad +2\n\\end{align*}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

    \"i\hbar\frac{\partial}{\partial<\/p>\n\n\n\n

    i<\/mi>\u210f<\/mi>\u2202<\/mi>\u2202<\/mi>t<\/mi><\/mrow><\/mfrac>|<\/mo>\u03a8<\/mi><\/mrow>(<\/mo>t<\/mi>)<\/mo>\u27e9<\/mo><\/mrow>=<\/mo>H<\/mi>|<\/mo>\u03a8<\/mi><\/mrow>(<\/mo>t<\/mi>)<\/mo>\u27e9<\/mo><\/mrow><\/mrow>i\\hbar\\frac{\\partial}{\\partial t}\\left|\\Psi(t)\\right>=H\\left|\\Psi(t)\\right><\/annotation><\/semantics><\/math><\/div>\n","protected":false},"excerpt":{"rendered":"

    IPv4 addresses 232=4,294,967,2962^{32}=4,294,967,296 n 27262524232221202^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 Assignable IP addresses 2h\u221222^h-2 Subnets 2s2^s block size 256\u2212InterestingOctet256-Interesting Octet 248\u00f72=124 124\u00f72=62124\u00f72=62124\u00f72=62 1: 124\u00f72=62124\u00f72=6262\u00f72=3131\u00f72=1515\u00f72=77\u00f72=33\u00f72=11\u00f72=0124\u00f72 =62\\\\ 124\u00f72=62\\\\ 62\u00f72=31\\\\ 31\u00f72=15\\\\ 15\u00f72=7\\\\ 7\u00f72=3\\\\ 3\u00f72=1\\\\ 1\u00f72=0 Total IPv6 2128=3.4×10382^{128}=3.4×10^{38} slope-intercept form: y=mx+by=mx+b ; standard quadratic form: ax2+bx+c=0ax^2+bx+c=0 ; quadratic forumal: x=\u2212b\u00b1b2\u22124ac2ax=\\frac{-b \\pm \\sqrt{b^2-4ac}}{2a} speed: S=rtS=rt; distance: time:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"pagelayer_contact_templates":[],"_pagelayer_content":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-399","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-uncategorized"},"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/peQefU-6r","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/edk-tech.net\/index.php?rest_route=\/wp\/v2\/posts\/399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/edk-tech.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/edk-tech.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/edk-tech.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/edk-tech.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=399"}],"version-history":[{"count":1,"href":"https:\/\/edk-tech.net\/index.php?rest_route=\/wp\/v2\/posts\/399\/revisions"}],"predecessor-version":[{"id":1323,"href":"https:\/\/edk-tech.net\/index.php?rest_route=\/wp\/v2\/posts\/399\/revisions\/1323"}],"wp:attachment":[{"href":"https:\/\/edk-tech.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=399"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/edk-tech.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=399"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/edk-tech.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}