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Binary Numbers

Background

Binary Notation

Writing numbers in binary notation means expressing them as a sequence of binary digits (bits), either 0 or 1. Each number must be represented by powers of two. Counting from the left, the position represents the exponent of this power.

 

For example, in binary, we can write the number 155 into powers of two, as shown below:

 

155  =128+16+8+2+1 = 27+24+23+21+20= 127+026+025+124+123+022+121+120   =10011011 (in binary)

Binary Numbers in Digital Electronics

Digital electronics, such as digital computers, are made up of electronic circuits. These electronic circuits have only two states: on and off. How are computers then able to perform the complex operations they do? The underlying communications interface for computers is binary. The states on and off can be represented by the bits 1 and 0, respectively. These bits can be used in sequence to create a base two "binary" number system analogous to our base ten "decimal" number system. Various combinations of these binary bits are used in computing to represent various items, such as pictures and videos. Furthermore, computers are able to perform arithmetic operations on these binary numbers and can even employ Boolean algebra, which is a subsection of algebra dealing with only two states. Moreover, signals with binary representations can be generated and used by computers to communicate with other devices. Although there are many different types of computers, all of them use the same underlying binary language.

One night, you are fishing in your motorboat when you get a distress signal on the radio that a ship has sunk. The passengers are clinging onto buoys in the water. However, not all the buoys are being occupied by passengers and it is too dark for you to see if one is being occupied. Fortunately, there is a lighthouse on a nearby shore that has a clear view of the scene and can help you see which buoys are occupied. The buoys each have a distinct number written on them, but to communicate the number to you, the lighthouse has to use its light as a signal. You quickly figure out that the lighthouse will be telling you the number of the buoy in binary, using a light pulse as a binary 1 and no light as a binary 0. You must translate the code back into decimal form to determine which buoy to travel to. To make matters worse, you see a giant wave approaching in the distance. Can you save all the people before the wave hits?

 

Choose the difficulty of the game and then press start. Click anywhere on the plot to move the boat to that location. If you successfully rescue a passenger, you will gain three seconds of time before the wave hits, but if you stop on a buoy that does not have a passenger, you will lose six seconds of time.

 

Shipwrecked

A Binary To Decimal

Conversion Game

 

 

Choose Difficulty:

 

 

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