Binary Numbers
Binary numbers allow the representation of any amount using just the two digits:0 and 1. Here are some examples of binary numbers…
Decimal 1 is binary 0001
Decimal 3 is binary 0011
Each digit “1” in a binary number system represents a power of two, and each “0” represents zero. For example:
0001 is 2 to the zero power (2^0 = 1)
0010 is 2 to the 1st power, or 2
0100 is 2 to the 2nd power, or 4
1000 is 2 to the 3rd power, or 8
You can also use this idea to binary count using your fingers, the binary number system knowledge is mainly useful for computing and implemented into programs since they are simple to work with. For example, if creating a large program which stores many integers, the program would be more efficient if it stored those integers as a binary number instead. This is a valuable skill to make complicated programs more simplistic.
What do you do when converting binary numbers such as “0101”?
You can simply add the powers of 2:
0101 = 0 + 4 + 0 + 1 = 5 (decimal value).
When representing bigger whole numbers (integers), you need more bits which is more columns or places in the binary number. Upon reaching 8 bits (the equivalent of one byte) there is 8 places in the binary number which results in the decimal number 255.
1-15 in the decimal and binary number systems.
Why Use Binary Number Systems?
- they are simple to work with — no big addition tables and multiplication tables to learn
- they just use two values of signals, voltage etc. (zero or one). This makes the hardware easier to design and more noise resistant
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