{"id":186,"date":"2006-10-12T22:14:08","date_gmt":"2006-10-12T22:14:08","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2006\/10\/12\/who-needs-a-calculator-multiplying-with-your-fingers\/"},"modified":"2006-10-12T22:14:08","modified_gmt":"2006-10-12T22:14:08","slug":"who-needs-a-calculator-multiplying-with-your-fingers","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2006\/10\/12\/who-needs-a-calculator-multiplying-with-your-fingers\/","title":{"rendered":"Who needs a calculator? Multiplying with Your Fingers"},"content":{"rendered":"<p>To do multiplication with your fingers in binary is very easy: it&#8217;s just a mixture of addition and bit-shifting. The only real trick is memory: to multiply a&times;b, you need to remember the binary digits of both x and y, which can be a bit of a trick for 10 digit binary numbers.<br \/>\nThe trick that I like is to use coins. Lay out a bunch of coins: one for each binary digit of a, and one for each binary digit of b. Put two lines on a piece of paper: one line will be the ones, the other will be the zeros. So, for example, to multiple 47 times 24, you&#8217;d start with the following:<br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" alt=\"finger-mult-setup.jpg\" src=\"https:\/\/i0.wp.com\/scientopia.org\/img-archive\/goodmath\/img_86.jpg?resize=266%2C87\" width=\"266\" height=\"87\" \/><br \/>\nThe coins on the paper are your guide, to help you remember the two numbers you&#8217;re multiplying. Now the basic algorithm. You start with zero on your fingers; then, starting with the *largest* digit of *B*:<br \/>\n1. Take the current sum on your hands, and multiply it by two. Multiplying by<br \/>\ntwo is just a simple shift operation &#8211; shift each digit up to the next highest<br \/>\nposition.<br \/>\n2. If the current digit is &#8220;1&#8221;, then add &#8220;A&#8221; to what&#8217;s on your fingers.<br \/>\n3. Move to the next digit of &#8220;B&#8221;.<br \/>\nSo, for example:<br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" alt=\"binary-finger-mult.jpg\" src=\"https:\/\/i0.wp.com\/scientopia.org\/img-archive\/goodmath\/img_87.jpg?resize=437%2C485\" width=\"437\" height=\"485\" \/><br \/>\nThat&#8217;s all there is to it. It&#8217;s really easy; once you&#8217;ve<br \/>\ngotten used to doing binary addition on your fingers, moving<br \/>\nto multiplication this way is very straightforward and<br \/>\nmechanical.<br \/>\nFor the particularly clever folks out there, you&#8217;ll notice that this is<br \/>\npretty much the same algorithm that we used for [multiplying roman numerals](http:\/\/scienceblogs.com\/goodmath\/2006\/08\/roman_numerals_and_arithmetic.php).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>To do multiplication with your fingers in binary is very easy: it&#8217;s just a mixture of addition and bit-shifting. The only real trick is memory: to multiply a&times;b, you need to remember the binary digits of both x and y, which can be a bit of a trick for 10 digit binary numbers. The trick [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_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":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[34],"tags":[],"class_list":["post-186","post","type-post","status-publish","format-standard","hentry","category-manual-computing-devices"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-30","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=186"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/186\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=186"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}