The numeric system we use daily is the decimal system, but this system is not convenient for machines since the information is handled codified in the shape of on or off bits, this way of codifying takes us to the necessity of knowing the positional calculation which will allow us to express a number is any base where we need it.<\/p>\n
A base of a number system or radices defines the range of values that a digit may have.<\/p>\n
1. In the binary system or base 2, there can be only two values for each digit of a number, either a \u201c0\u201d
\nor a \u201c1\u201d.
\n2. In the octal system or base 8, there can be eight choices for each digit of a number:
\n\u201c0\u201d, \u201c1\u201d, \u201c2\u201d, \u201c3\u201d, \u201c4\u201d, \u201c5\u201d, \u201c6\u201d, \u201c7\u201d
\n3. In the decimal system or base 10, there are ten different values for each digit of a number:
\n\u201c0\u201d, \u201c1\u201d, \u201c2\u201d, \u201c3\u201d, \u201c4\u201d, \u201c5\u201d, \u201c6\u201d, \u201c7\u201d, \u201c8\u201d, \u201c9\u201d
\n4. In the hexadecimal system, we allow 16 values for each digit of a number:
\n\u201c0\u201d, \u201c1\u201d, \u201c2\u201d, \u201c3\u201d, \u201c4\u201d, \u201c5\u201d, \u201c6\u201d, \u201c7\u201d, \u201c8\u201d, \u201c9\u201d, \u201cA\u201d, \u201cB\u201d, \u201cC\u201d, \u201cD\u201d and \u201cF\u201d
\nwhere \u201cA\u201d stands for 10, \u201cB\u201d for 11 and so on.
\nIn general, a positive number N can be written in positional notation as<\/p>\n
N=(an \u2013 1 an \u2013 2 … a1 a0 . a\u20131 a\u20132 … a\u2013m)<\/p>\n
where,<\/p>\n
. = radix point separating the integer and fractional digits.
\nr = radix or base of the number system being used
\nn = number of integer digits to the left of the radix point
\nm=number of fractional digits to the right of the radix point
\nai = integer digits i when n \u2013 1 \u2265 i \u2265 0
\naj = fractional digits j when \u20131 \u2265 i \u2265 \u2013m
\nan \u2013 1 = most significant digit
\nan \u2013 2 = least significant digit<\/p>\n
A number system with base or radix \u2018r\u2019 will have r number of different digits from 0 \u2192 (r\u2013 1) thus, number system is represented by (N)b
\nwhere,
\nN= Number ; b = Base or radix<\/p>\n","protected":false},"excerpt":{"rendered":"
The numeric system we use daily is the decimal system, but this system is not convenient for machines since the<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,1948],"tags":[1950,1949],"class_list":["post-6563","post","type-post","status-publish","format-standard","hentry","category-cs-it","category-digital-logic","tag-radices","tag-radix-number-system"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/6563","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=6563"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/6563\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=6563"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=6563"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=6563"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}