{"id":7728,"date":"2018-02-19T08:33:46","date_gmt":"2018-02-19T08:33:46","guid":{"rendered":"https:\/\/assignment.essayshark.com\/blog\/?p=7728"},"modified":"2022-01-05T11:13:50","modified_gmt":"2022-01-05T11:13:50","slug":"cryptography-examples-hamming-code-in-practice","status":"publish","type":"post","link":"https:\/\/assignmentshark.com\/blog\/cryptography-examples-hamming-code-in-practice\/","title":{"rendered":"Cryptography Examples: Hamming Code in Practice"},"content":{"rendered":"

Assignments on cryptography may be sometimes hard to understand. To help our students achieve deep understanding in cryptography, one of our writers has picked a task on Hamming code and described its solution. Take a look at our <\/span><\/i>cryptography examples <\/i>and observe how the author came to the particular solution. All of our sample papers are free of charge and are aimed to help students with studying new material.<\/span><\/i><\/p>\n

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 <\/p><\/blockquote>\n

Task:<\/b><\/u><\/p>\n

Using the Hamming code, find the error in the message: 1001 0001 1101 1110 0000 000.<\/span><\/p>\n

Solution:<\/b><\/u><\/p>\n

The message length is 27 digits; from them 22 are informational and 5 are control.<\/span><\/p>\n

Control digits are b1 = 1, b2 = 1, b4 = 1, b8 = 1, b16=0.<\/span><\/p>\n

Let\u2019s calculate the number of J for error detection.<\/span><\/p>\n

For convenience, let\u2019s introduce the following sets:<\/span><\/p>\n

V1 = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27\u2026 – all numbers whose first digit is equal to 1;<\/span><\/p>\n

V2 = 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27\u2026 – all numbers whose second digit is equal to 1;<\/span><\/p>\n

V3 = 4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28\u2026 – all numbers whose third digit is equal to 1;<\/span><\/p>\n

V4 = 8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28\u2026 – all numbers whose fourth digit is equal to 1;<\/span><\/p>\n

V5 = 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 \u2026 – all numbers whose fifth digit is equal to 1.<\/span><\/p>\n

Digits numbered J are defined as follows:<\/span><\/p>\n

j1 = b1 + b3+b5+b7+b9+b11+b13+b15+b17+b19+b21+b23+b25+b27 = 1;<\/span><\/p>\n

j2 = b2+ b3+b6+b7+b10+b11+b14+ b15+ b18+ b19+ b22+ b23+ b26+ b27= 0;<\/span><\/p>\n

j3 = b4+ b5+b6+b7 +b12+b13+ b14+ b15+ b20 +b21+b22+b23 = 0;<\/span><\/p>\n

j4 = b9+b10+b11+b12+b13+b14+b15+b24+b25+b26+b27 = 0;<\/span><\/p>\n

j5 = b16+ b17+b18+b19+b20+b21+b22+b23+b24+b25+b26+b27 = 1,<\/span><\/p>\n

so the number <\/span>J = <\/span><\/i>10001 <\/span>2<\/sub> \u00a0<\/span>\u00a0= \u00a0<\/span><\/i>17<\/span>10<\/sub><\/span> .<\/span><\/p>\n

Thus, an error occurred in the seventeenth digit of the transferred number and 1 should be replaced to 0. Then we obtain 1111 1011 0010 1100 0101 1100 110.<\/span><\/p>\n

Now let\u2019s remove the control digits. We get 1101 0010 1100 1011 1001 10 \u2013 the transmitted number.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Assignments on cryptography may be sometimes hard to understand. To help our students achieve deep understanding in cryptography, one of our writers has picked a task on Hamming code and described its solution. Take a look at our cryptography examples and observe how the author came to the particular solution. All of our sample papers […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[53,35],"tags":[],"class_list":["post-7728","post","type-post","status-publish","format-standard","hentry","category-it","category-samples"],"_links":{"self":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts\/7728","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/comments?post=7728"}],"version-history":[{"count":14,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts\/7728\/revisions"}],"predecessor-version":[{"id":12883,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts\/7728\/revisions\/12883"}],"wp:attachment":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/media?parent=7728"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/categories?post=7728"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/tags?post=7728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}