In mathematics and digital electronics, a binary number is a number expressed in the binary numeral system, or base-2 numeral system, which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2 system is apositional notation with a radix of 2.
Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit.
Example of Addition in Binary
1 1 1 1 1 (carried digits)
0 1 1 0 1
+ 1 0 1 1 1
------------- =
1 0 0 1 0 0 = 36
Registers and different numbers that can be represented
Using 4 bits there are 24 (16) different combinations of zeros and ones, 0000 being the smallest and 1111 the largest.
Generaly it is found by
(number of available bits) to the exponent of (number of available positions - register)
There is a simple formula to work out the largest decimal number that can be represented by a certain number of bits all set to 1. It is 2 to the power of the number of bits minus 1. One is taken off because the system starts at 0. So, using four bits the following decimal numbers can be represented: 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. This is sixteen numbers in all.
Particular bit patterns have names. Four bits is called a nibble, eight bits is called a byte, four bytes is called a word. Using the formula above a byte can represent a maximum decimal value of 28 - 1, or 255.
Different systems within a computer can use different numbers of bits. For example, most modern processors can read/write 64 bits of data at a time from/to RAM, whereas the Windows 7 operating system comes in both 32 and 64 bit versions. For various reasons the 32 bit version limits the amount of RAM it can address to around 3 Gigabytes, so anything above this figure is useless.
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Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit.
Example of Addition in Binary
1 1 1 1 1 (carried digits)
0 1 1 0 1
+ 1 0 1 1 1
------------- =
1 0 0 1 0 0 = 36
Registers and different numbers that can be represented
Using 4 bits there are 24 (16) different combinations of zeros and ones, 0000 being the smallest and 1111 the largest.
Generaly it is found by
(number of available bits) to the exponent of (number of available positions - register)
There is a simple formula to work out the largest decimal number that can be represented by a certain number of bits all set to 1. It is 2 to the power of the number of bits minus 1. One is taken off because the system starts at 0. So, using four bits the following decimal numbers can be represented: 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. This is sixteen numbers in all.
Particular bit patterns have names. Four bits is called a nibble, eight bits is called a byte, four bytes is called a word. Using the formula above a byte can represent a maximum decimal value of 28 - 1, or 255.
Different systems within a computer can use different numbers of bits. For example, most modern processors can read/write 64 bits of data at a time from/to RAM, whereas the Windows 7 operating system comes in both 32 and 64 bit versions. For various reasons the 32 bit version limits the amount of RAM it can address to around 3 Gigabytes, so anything above this figure is useless.
-> For more reading click here.