A 32 binary number is a number stored by a computer in 32 bits. it can represent:
1) An unsigned number in the range 0 to 4,294,967,295
2) A signed number in the range -2,147,483,648 to 2,147,483,647
3) A single precision IEEE floating point number with 1 sign bit, 8 exponent bits and 23 mantissa bits give an accuracy of about 7.2 decimal digits and a range of ± 10^-38 to 10^38
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hexadecimal can express 16 bit binary in 4 place form, not 16.
The root of the tree is stored in array element [0]; for any node of the tree that is stored in array element [i], its left child is stored in array element [2*i], its right child at [2*i+2]
Not to be flippant, but every file is an example of data encoding. Before data can be stored in computer memory or in a disk file, it first has to be digitally encoded in binary. The binary encodings can then be further encoded using encryption or compression.
Your question is actually flawed...binary system is not used in digital systems... Rather, systems using binary numbers only are called digital systems... It is common knowledge that, digital electronics employs just 2 states (or rather numbers, as mathematicians put it...) the two numbers being '0' and '1'. Obviously, it is easier to design electronic systems dealing with just 2 states...It's majorly this ease, that led to such exponential development in the field of digital electronics. It ios also cheaper to make or produce such systems...
The very lowest possible level at which you can program a computer is in its own native machine code, consisting of strings of 1's and 0's and stored as binary numbers. The main problems with using machine code directly are that it is very easy to make a mistake, and very hard to find it once you realize the mistake has been made.