The result is this collection of excel calculators & cheat sheets. This article was provided by Life's Little Mysteries, a sister site to LiveScience. Follow Natalie Wolchover on Twitter nattyover.Anytime I have to do the same calculation twice I start thinking about how to automate the process. Such calculations take more time, but still no more than the blink of an eye. To perform more complex calculations, such as multiplying or dividing huge numbers, a calculator performs a long series of simple additions and subtractions, all of which occur much like the above description of 2+2. Sure enough, when 100 (representing 4) is sent through the array of logic gates associated with that top bar, the end result will be a 0 - a "don't darken the bar" command.Īll this circuitry happens in a flash, producing a 4 on the display seemingly instantaneously. To make a 4, for example, the top bar does not need to be darkened. In binary code, 100 represents 4.Īdditional logic gates "figure out" whether or not to darken the various sections used to form the shapes of numbers - typically composed of seven bars arranged as a digital figure eight - on the calculator screen. The final outputted signals are 1, 0 and 0. In a process similar to "carrying the ten's place" in regular addition, the output from the 0s' AND gate gets combined with the output from the 1s' XOR gate: The 0 and 0 are sent through an OR gate, resulting in a 0. The original 0s (from 10 and 10) are also sent to AND and XOR gates, which both produce outputs of 0. Since both inputs are 1, the XOR gate outputs a 0. Even the simple operation of adding those numbers together requires a complicated array of logic gates, but here's the gist of the process: Logic gates are used to combine the information stored in the two pairs of transistors - 10 and 10 (representing 2 and 2). OR sends out a 1 if either or both of its inputs is a 1, whereas XOR only outputs a 1 if its inputs are 1 and 0. The NOT gate switches the incoming signal: if its input is 1, its output is 0, and vice versa. But if it receives a 1 and a 0, or two 0s, it sends out a 0. Take the AND gate: If both the signals that arrive at the gate are 1s, then AND sends out a 1. Together, the logic gates enable circuits to add, subtract, multiply and divide the numbers sent to them by transistors. There are several types of logic gates: AND, OR, NOT and XOR (exclusive OR). As the name implies, a logic gate acts as a barrier in an electronic circuit it takes in two electric currents, compares them and sends out a new current based on what it finds. Now the calculator must add those inputs together.Ĭalculators (and computers) combine inputs using electronic components called logic gates. Two of its transistors (in the 10 configuration) correspond to the first "2" you pressed, and another pair of transistors, also in the 10 position, corresponds to the second number 2. Now the calculator has the go-ahead to execute the previously entered "+" command. You press "2." Just like they did the first time, electric currents translate your "2" into binary code, by switching one transistor on and another off.įinally, you press the "=" button. The rubber underneath it smashes two wires into contact, causing electricity to flow in such a way that the first input (the "2") gets stored, the addition function is signaled, and the calculator is ready for a new input.
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