{"id":2295,"date":"2017-06-15T22:02:41","date_gmt":"2017-06-15T22:02:41","guid":{"rendered":"http:\/\/10.10.10.4:9191\/softlect\/?p=2295"},"modified":"2019-10-22T20:45:02","modified_gmt":"2019-10-22T20:45:02","slug":"converting-decimal-binary-octal-hexadecimal","status":"publish","type":"post","link":"http:\/\/softlect.com\/index.php\/converting-decimal-binary-octal-hexadecimal\/","title":{"rendered":"Converting Decimal, Binary, Octal, Hexadecimal"},"content":{"rendered":"

Numeral Systems Conversion Table<\/h2>\n
\n
\n
Decimal Base-10<\/strong><\/div>\n
Binary Base-2<\/strong><\/div>\n
Octal Base-8<\/strong><\/div>\n
Hexadecimal Base-16<\/strong><\/div>\n<\/div>\n
\n
0<\/div>\n
0<\/div>\n
0<\/div>\n
0<\/div>\n<\/div>\n
\n
1<\/div>\n
1<\/div>\n
1<\/div>\n
1<\/div>\n<\/div>\n
\n
2<\/div>\n
10<\/div>\n
2<\/div>\n
2<\/div>\n<\/div>\n
\n
3<\/div>\n
11<\/div>\n
3<\/div>\n
3<\/div>\n<\/div>\n
\n
4<\/div>\n
100<\/div>\n
4<\/div>\n
4<\/div>\n<\/div>\n
\n
5<\/div>\n
101<\/div>\n
5<\/div>\n
5<\/div>\n<\/div>\n
\n
6<\/div>\n
110<\/div>\n
6<\/div>\n
6<\/div>\n<\/div>\n
\n
7<\/div>\n
111<\/div>\n
7<\/div>\n
7<\/div>\n<\/div>\n
\n
8<\/div>\n
1000<\/div>\n
10<\/div>\n
8<\/div>\n<\/div>\n
\n
9<\/div>\n
1001<\/div>\n
11<\/div>\n
9<\/div>\n<\/div>\n
\n
10<\/div>\n
1010<\/div>\n
12<\/div>\n
A<\/div>\n<\/div>\n
\n
11<\/div>\n
1011<\/div>\n
13<\/div>\n
B<\/div>\n<\/div>\n
\n
12<\/div>\n
1100<\/div>\n
14<\/div>\n
C<\/div>\n<\/div>\n
\n
13<\/div>\n
1101<\/div>\n
15<\/div>\n
D<\/div>\n<\/div>\n
\n
14<\/div>\n
1110<\/div>\n
16<\/div>\n
E<\/div>\n<\/div>\n
\n
15<\/div>\n
1111<\/div>\n
17<\/div>\n
F<\/div>\n<\/div>\n
\n
16<\/div>\n
10000<\/div>\n
20<\/div>\n
10<\/div>\n<\/div>\n
\n
17<\/div>\n
10001<\/div>\n
21<\/div>\n
11<\/div>\n<\/div>\n
\n
18<\/div>\n
10010<\/div>\n
22<\/div>\n
12<\/div>\n<\/div>\n
\n
19<\/div>\n
10011<\/div>\n
23<\/div>\n
13<\/div>\n<\/div>\n
\n
20<\/div>\n
10100<\/div>\n
24<\/div>\n
14<\/div>\n<\/div>\n
\n
21<\/div>\n
10101<\/div>\n
25<\/div>\n
15<\/div>\n<\/div>\n
\n
22<\/div>\n
10110<\/div>\n
26<\/div>\n
16<\/div>\n<\/div>\n
\n
23<\/div>\n
10111<\/div>\n
27<\/div>\n
17<\/div>\n<\/div>\n
\n
24<\/div>\n
11000<\/div>\n
30<\/div>\n
18<\/div>\n<\/div>\n
\n
25<\/div>\n
11001<\/div>\n
31<\/div>\n
19<\/div>\n<\/div>\n
\n
26<\/div>\n
11010<\/div>\n
32<\/div>\n
1A<\/div>\n<\/div>\n
\n
27<\/div>\n
11011<\/div>\n
33<\/div>\n
1B<\/div>\n<\/div>\n
\n
28<\/div>\n
11100<\/div>\n
34<\/div>\n
1C<\/div>\n<\/div>\n
\n
29<\/div>\n
11101<\/div>\n
35<\/div>\n
1D<\/div>\n<\/div>\n
\n
30<\/div>\n
11110<\/div>\n
36<\/div>\n
1E<\/div>\n<\/div>\n
\n
31<\/div>\n
11111<\/div>\n
37<\/div>\n
1F<\/div>\n<\/div>\n
\n
32<\/div>\n
100000<\/div>\n
40<\/div>\n
20<\/div>\n<\/div>\n<\/div>\n

 <\/p>\n

The examples of the Decimal, Binary, Octal and Hexadecimal number systems are described below:<\/p>\n

Decimal Number System (Base 10):<\/h3>\n

Decimal numbers use digits from 0 to 9<\/p>\n

Example:<\/strong><\/p>\n

253810<\/sub>\u00a0= 2\u00d7103<\/sup>+5\u00d7102<\/sup>+3\u00d7101<\/sup>+8\u00d7100<\/sup><\/p>\n

 <\/p>\n

Binary Number System (Base 2):<\/h3>\n

Binary Numbers uses only 0 and 1 digits<\/p>\n

Example:<\/strong><\/p>\n

101012<\/sub> = 10101 = 1\u00d724<\/sup>+0\u00d723<\/sup>+1\u00d722<\/sup>+0\u00d721<\/sup>+1\u00d720 <\/sup>= 16+4+1= 21<\/p>\n

101112<\/sub> = 10111 = 1\u00d724<\/sup>+0\u00d723<\/sup>+1\u00d722<\/sup>+1\u00d721<\/sup>+1\u00d720 <\/sup>= 16+4+2+1= 23<\/p>\n

1000112<\/sub> = 100011 = 1\u00d725<\/sup>+0\u00d724<\/sup>+0\u00d723<\/sup>+0\u00d722<\/sup>+1\u00d721<\/sup>+1\u00d720<\/sup>=32+2+1= 35<\/p>\n

 <\/p>\n

Octal Number System (Base 8):<\/h3>\n

Octal numbers use digits from 0 to 7<\/p>\n

Example:<\/strong><\/p>\n

278<\/sub>\u00a0= 2\u00d781<\/sup>+7\u00d780\u00a0<\/sup>= 16+7 = 23<\/p>\n

308<\/sub>\u00a0= 3\u00d781<\/sup>+0\u00d780\u00a0<\/sup>= 24<\/p>\n

43078<\/sub>\u00a0= 4\u00d783<\/sup>+3\u00d782<\/sup>+0\u00d781<\/sup>+7\u00d780<\/sup>= 2247<\/p>\n

 <\/p>\n

Hexadecimal Number System (Base 16)<\/h3>\n

Hexa numbers use digits from 0 to 9 and A to F<\/p>\n

Example:<\/strong><\/p>\n

2816<\/sub>\u00a0= 28 = 2\u00d7161<\/sup>+8\u00d7160\u00a0<\/sup>= 40<\/p>\n

2F16<\/sub>\u00a0= 2F = 2\u00d7161<\/sup>+15\u00d7160\u00a0<\/sup>= 47<\/p>\n

BC1216<\/sub>\u00a0= BC12 = 11\u00d7163<\/sup>+12\u00d7162<\/sup>+1\u00d7161<\/sup>+2\u00d7160<\/sup>= 48146<\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Digital Systems uses a variety of different number systems, (e.g. Decimal, Hexadecimal, Octal, Binary). A number system is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. <\/p>\n","protected":false},"author":1,"featured_media":3610,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[70],"tags":[],"aioseo_notices":[],"amp_enabled":true,"_links":{"self":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2295"}],"collection":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/comments?post=2295"}],"version-history":[{"count":40,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2295\/revisions"}],"predecessor-version":[{"id":3342,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2295\/revisions\/3342"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media\/3610"}],"wp:attachment":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media?parent=2295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/categories?post=2295"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/tags?post=2295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}