### What is the binary number system?

It is crucial that before learning about computers, one understands the binary number system. The binary number system is a different way to look at numbers and represents values only using the digits one and zero. Most computing devices use this number system. A computer is made up of electrical devices, so it couldn't use paper to keep track of data. Instead, it uses voltages. A one is represented by a high voltage, while a zero is represented by a low voltage. Counting in binary is much the same as counting in decimal in that when you count past the highest digit, you put down a zero and carry over a one to the next column. If you were to start counting from zero to ten, the binary sequence would look like this:

Binary
`00000000, 00000001, 00000010, 00000011, 00000100,...00001001, 00001010`
Decimal
`       0,        1,        2,        3,        4,...       9,       10`

As you can see, the numbers look different but still represent the same values. All of the tasks that a computer does are simply manipulations of numbers that have been converted to the binary system and are represented by voltages. In order to represent negative numbers, the last (left-most) bit is reserved to indicate the sign of the number. In the above eight bit numbers, 11111111 would be -1 and 10000000 would be -128. It might seem easier to have it work so that 10000001 was -1 and 11111111 was -127, but consider adding 10000001 and 00000001 (-1 + 1). The normal process of adding and carrying would not work here, since the desired result is 00000000. But 11111111+00000001 gives 100000000. The computer would only be using the first eight bits, so the last 1 would be lost, yeilding 00000000, the zero that is expected. Besides, the other numbering system would have two zeros, one positive, and one negative. This could pose problems when comparing two numbers (are -0 and +0 equal? do we want them to be?).

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