{"id":924,"date":"2022-01-31T17:35:03","date_gmt":"2022-01-31T17:35:03","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=924"},"modified":"2022-01-31T17:35:03","modified_gmt":"2022-01-31T17:35:03","slug":"binary-numbers","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/01\/31\/binary-numbers\/","title":{"rendered":"Binary Numbers"},"content":{"rendered":"\n

Summary <\/strong><\/p>\n\n\n\n

The binary number system is a base-2 number system. This means it only has two numbers: 0 and 1. The number system that we normally use is the decimal number system. It has 10 numbers: 0-9. <\/p>\n\n\n\n

Why use binary numbers? <\/h5>\n\n\n\n

Binary numbers are very useful in electronics and computer systems. Digital electronics can easily work with a sort of “on” or “off” system where “on” is a 1 and “off” is a zero. Often times the 1 is a “high” voltage, while the 0 is a “low” voltage or ground. <\/p>\n\n\n\n

How do binary numbers work? <\/h5>\n\n\n\n

Binary numbers only use the numbers 1 and 0. In a binary number each “place” represents a power of 2.<\/p>\n\n\n\n

For example: <\/h4>\n\n\n\n

1 = 20<\/sup> = 1 <\/p>\n\n\n\n

10 = 21<\/sup> = 2 <\/p>\n\n\n\n

100 = 22<\/sup> = 4 <\/p>\n\n\n\n

1000 = 23<\/sup> = 8 <\/p>\n\n\n\n

10000 = 24<\/sup> = 16<\/p>\n\n\n\n

Converting from Binary to Decimal<\/h2>\n\n\n\n

If you want to convert a number from binary to decimal, you can add up the “places” that we showed above. Each place that has a “1” represents a power of 2, starting with the 0s place. <\/p>\n\n\n\n

Examples: <\/p>\n\n\n\n

101 binary = 4 + 0 + 1 = 5 decimal<\/p>\n\n\n\n

11110 binary = 16 + 8 + 4 + 2 + 0 = 30 decimal <\/p>\n\n\n\n

10001 binary = 16 + 0 + 0 + 0 + 1 = 17 decimal <\/p>\n\n\n\n

Converting from Decimal to Binary <\/h2>\n\n\n\n

Converting a decimal number to a binary number can be more difficult. It helps if you know the powers of two (1, 2, 4, 8, 16, 32, 64, 128, 256, \u2026). <\/p>\n\n\n\n

  • First subtract the largest power of two possible from the number you are converting. <\/li>
  • Then put a “1” in that place of the binary number.<\/li>
  • Next, you subtract the next biggest power of two possible from the remainder. You put a 1 in that position. <\/li>
  • You keep repeating the above until there is no remainder left. <\/li>
  • All the places without a “1” get a “0”. <\/li><\/ul>\n\n\n\n

    <\/p>\n\n\n\n

    Example:<\/h4>\n\n\n\n

    What is 27 decimal in binary?<\/h5>\n\n\n\n
    1. What is the largest power of 2 that is less than or equal to 27? That is 16. So subtract 16 from 27. 27 – 16 = 11 <\/li>
    2. Put a 1 in the 16’s place. That is 24<\/sup>, which is the 5th place because it starts with the 0’s place. So we have 1xxxx so far. <\/li>
    3. Now do the same for the remainder, 11. The largest power of two number we can subtract from 11 is 23<\/sup>, or 8. So, 11 – 8 = 3. <\/li>
    4. Put a 1 in the 8’s place. Now we have 11xxx. <\/li>
    5. Next is to subtract 21<\/sup>, or 2 which is 2 -1 = 1. <\/li>
    6. 11x1x <\/li>
    7. Lastly is 1-1 = 0. <\/li>
    8. 11×11 9. Put zero’s in the places without 1’s and we get the answer = 11011. <\/li><\/ol>\n\n\n\n

      <\/p>\n\n\n\n

      Other examples:<\/p>\n\n\n\n

      14 = 8 + 4 + 2 + 0 = 1110<\/p>\n\n\n\n

      21 = 16 + 0 + 4 + 0 + 1 = 10101 <\/p>\n\n\n\n

      44 = 32 + 0 + 8 + 4 + 0 + 0 = 101100 <\/p>\n\n\n\n

      Helpful Binary Tables First 10<\/p>\n\n\n\n

      \"\"\/<\/figure>\n\n\n\n

      Numbers Binary Position Values in Decimal (powers of 2)<\/p>\n\n\n\n

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

      Summary The binary number system is a base-2 number system. This means it only has two numbers: 0 and 1. The number system that we normally use is the decimal number system. It has 10 numbers: 0-9. Why use binary numbers? Binary numbers are very useful in electronics and computer systems. Digital electronics can easily […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[565],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/924"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=924"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/924\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}