The digital computer is a digital system that performs various computational tasks. <\/p>\n\n\n\n
Generally the word digital means:<\/p>\n\n\n\n
The decimal digits 0, 1, 2, …, 9, for example, provide 10 discrete values.<\/p><\/blockquote><\/figure>\n\n\n\n
Here the word digital implies a system that can be used by a computer and other electronic equipment, in which information is sent and received in electronic form as a series of the numbers 1 and 0<\/strong><\/p>\n\n\n\n
The first electronic digital computers, developed in the late 1940s, were used primarily for numerical computations. In this case, the discrete elements are the digits (ie., 0, 1,2…9). From this application, the term digital computer has emerged.<\/p>\n\n\n\n
In practice, digital computers function more reliably if only two values are used. <\/p>\n\n\n\n
Why?<\/h3>\n\n\n\n
Computers don’t understand <\/strong>words or numbers the way we humans do. In the end, everything in the computer is represented by a binary electrical signal that registers data in one of two states: ON or OFF<\/p>\n\n\n\n
Any instructions you give to the computer gets converted to binary. Later gets stored, processed within the system. Output again will be presented in the format we humans can understand.<\/p>\n\n\n\n
This ON or OFF usaually represented with two numbers 0 and 1. <\/p>\n\n\n\n
It’s called binary numbers as it has only two numbers in this system.<\/p><\/blockquote><\/figure>\n\n\n\n
Digital computers use the binary number system, which has two digits: 0 and 1. A binary digit is called a bit. <\/p>\n\n\n\n
In digital computers, information is represented in groups of bits.<\/p>\n\n\n\n
- A group of eight bits is called a byte.<\/li>
- Most computer memories use words whose number of bits is a multiple of 8.<\/li>
- Thus a 16-bit word contains two bytes, and<\/li>
- a 32-bit word is made up of four bytes.<\/li><\/ul>\n\n\n\n
It is customary to refer to the number of words (or bytes) in a memory with one of the letters <\/p>\n\n\n\n
1 KB<\/strong> (kilobyte) is 210<\/sup> = 1024 bytes<\/strong>, <\/p>\n\n\n\n
1 MB<\/strong> (megabyte) is 220<\/sup> = 1024 Kilo bytes<\/strong>, <\/p>\n\n\n\n
1 GB<\/strong> (gigabyte) is 230<\/sup> = 1024 Mega bytes<\/strong>, etc.,<\/p>\n\n\n\n
By using various coding techniques, groups of bits can be made to represent not only binary numbers but also other discrete symbols, such as decimal digits or letters of the alphabet.<\/p><\/blockquote><\/figure>\n\n\n\n
By judicious use of binary arrangements and by using various coding techniques, the groups of bits are used to develop complete sets of instructions for performing various types of computations.<\/p>\n\n\n\n
In contrast to the common decimal numbers that employ the base 10 system, binary numbers use a base 2 system with two digits: 0 and 1.<\/p>\n\n\n\n
The decimal equivalent of a binary number can be found by expanding it into a power series with a base of 2. <\/p>\n\n\n\n
For example, the binary number 1001011 <\/strong>represents a quantity that can be converted to a decimal number by multiplying each bit by the base 2 raised to an integer power<\/strong> as follows:<\/p>\n\n\n\n
binary base positions<\/td> 26<\/sup>=64<\/td> 25<\/sup>=32<\/td> 24<\/sup>=16<\/td> 23<\/sup>=8<\/td> 22<\/sup>=4<\/td> 21<\/sup>=2<\/td> 20<\/sup>=1<\/td><\/tr> given binary number<\/td> 1<\/td> 0<\/td> 0<\/td> 1<\/td> 0<\/td> 1<\/td> 1<\/td><\/tr> multiply base positions with the respective binary digit<\/td> 1×64=64<\/td> 0x32=0<\/td> 0x16=0<\/td> 1×8=8<\/td> 0x4=0<\/td> 1×2=2<\/td> 1×1 =1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Total sum is 64+0=0+8+0+2+1 = 75<\/strong><\/p>\n\n\n\n
Thus the seven bits 1001011 represent a binary number whose decimal equivalent is 75. <\/p><\/blockquote><\/figure>\n\n\n\n
<\/p>\n\n\n\n
However, this same group of seven bits represents the letter K<\/strong> when used in conjunction with a binary code for the letters of the alphabet. <\/p>\n\n\n\n
It may also represent a control code for specifying some decision logic in a particular digital computer. <\/p>\n\n\n\n
In other words, groups of bits in a digital computer are used to represent many different things. <\/p>\n\n\n\n
This is similar to the concept that the same letters of an alphabet are used to construct different languages, such as English and French.<\/p><\/blockquote><\/figure>\n\n\n\n
<\/p>\n\n\n\n
Similarly, first few decimal equivalent for binary is given below.<\/p>\n\n\n\n
Decimal
number<\/th>Binary
number<\/th><\/tr>0<\/td> 0<\/td><\/tr> 1<\/td> 1<\/td><\/tr> 2<\/td> 10<\/td><\/tr> 3<\/td> 11<\/td><\/tr> 4<\/td> 100<\/td><\/tr> 5<\/td> 101<\/td><\/tr> 6<\/td> 110<\/td><\/tr> 7<\/td> 111<\/td><\/tr> 8<\/td> 1000<\/td><\/tr> 9<\/td> 1001<\/td><\/tr> 10<\/td> 1010<\/td><\/tr> 11<\/td> 1011<\/td><\/tr> 12<\/td> 1100<\/td><\/tr> 13<\/td> 1101<\/td><\/tr> 14<\/td> 1110<\/td><\/tr> 15<\/td> 1111<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Next<\/strong>:<\/p>\n\n\n\n
Memory and binary data<\/p>\n","protected":false},"excerpt":{"rendered":"
Computers don\u2019t understand words or numbers the way we humans do. In the end, everything in the computer is represented by a binary electrical signal that registers data in one of two states: ON or OFF<\/p>\n
Any instructions you give to the computer gets converted to binary. Later gets stored, processed within the system. Output again will be presented in the format we humans can understand.<\/p>\n
This ON or OFF usaually represented with two numbers 0 and 1. <\/p>\n","protected":false},"author":2,"featured_media":2398,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[293,475,2],"tags":[284,294,283],"class_list":["post-2321","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-computer-science-applocations","category-posts-in-english","category-information-technology","tag-bca-syllubus","tag-binary-basics","tag-computer-organisation-architecture"],"cp_meta_data":{"_edit_lock":["1629956324:2"],"_last_editor_used_jetpack":["block-editor"],"_edit_last":["2"],"_heateor_sss_meta":["a:2:{s:7:\"sharing\";i:0;s:16:\"vertical_sharing\";i:0;}"],"_jetpack_related_posts_cache":["a:1:{s:32:\"8f6677c9d6b0f903e98ad32ec61f8deb\";a:2:{s:7:\"expires\";i:1782455798;s:7:\"payload\";a:3:{i:0;a:1:{s:2:\"id\";i:2251;}i:1;a:1:{s:2:\"id\";i:320;}i:2;a:1:{s:2:\"id\";i:87;}}}}"],"_thumbnail_id":["2398"]},"jetpack_featured_media_url":"https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/12\/binary.jpg","jetpack-related-posts":[{"id":2251,"url":"https:\/\/themindpalace.in\/index.php\/2020\/12\/12\/computer-organisation-architecture\/","url_meta":{"origin":2321,"position":0},"title":"Computer Organisation & Architecture","author":"The Mind","date":"December 12, 2020","format":false,"excerpt":"Summary on organisation and architecture of computer The original purpose of building computers was computing. Without this, most of the computing disciplines today would be a branch of theoretical mathematics. Summary Computer Architecture describes what the computer does.Computer Organization describes how it does it. 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