Three or Six Hours of Math Tutoring from U.S. Best Tutors (Up to 63% Off)

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Knowledge is power, which is why locomotives run on burning encyclopedias. Chug toward new understandings with this Groupon.

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Pocket Calculators: Bite-Sized Binary

Doing math is much easier with a calculator in your hand, but what's really happening under those buttons? Read on to learn more about the complex calculations happening inside.

Few modern inventions are as taken for granted as the calculator. Today's calculators are so small as to be practically forgotten, tucked away in a pocket or the apps folder of a smartphone. But despite the compact size, a calculator's functions are surprisingly complex—the collaboration of several electronic circuits working together to arrive at something even as simple as 2+2. When a user presses the buttons of a calculator, a chip inside translates each input into a binary number—a series of 1s and 0s—which it can more easily store in memory and send through a variety of built-in functions. Each function exists on an integrated circuit with its own logic and assortment of tiny counting beans. At the end of the calculation, the processor translates the binary solution back into a legible number and sends it to the calculator display. Heck, even the display is controlled by binary logic, which is why the numbers commonly consist of segmented lines. Each part of every numeral can be turned on or off according to the processor's instructions.

All this work happens so quickly and seamlessly we barely think twice about it. But only a few decades ago, the digital calculator was a revolutionary device—a mash of circuits and displays the size of a cash register and the cost of a midsize car. Before the 1960s, the only tools used to make personal calculations were objects such as the abacus and, beginning in the early nineteenth century, a variety of crude mechanical computers that used wheels and cogs to carry about basic arithmetic. Sharp unveiled the first desktop calculator in 1964, but it wasn't until the development of the microprocessor a few years later that engineers could begin to create pocket-sized versions. Nevertheless, calculators remained an expensive novelty for quite some time. A 1971 commercial for the Sharp EL-8, one of the first handheld calculators, touts its "price tag to match"—the low, low price of $345.

In a Nutshell

Small groups of custom math tutoring for K-12 and college students led by certified teachers or degreed professionals

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