In mathematics and digital electronics, a

1 1 1 1 1 (carried digits)

0 1 1 0 1

+ 1 0 1 1 1

------------- =

1 0 0 1 0 0 = 36

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

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.

**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.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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