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:
00000000, 00000001, 00000010, 00000011, 00000100,...00001001, 00001010
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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