# Binary De de-deity Conversion

Binary de de-deprecate conversion uses weighted bases, also known as columns, to determine the final value of the number and the order of numbers.

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The depreceence of the binary number (base-2 to base-10) and its recycling is an important concept to know as the binary numbering system forms the basis of all computer and digital systems.

The decimal or "decimal" counting system takes one of ten possible values, called "digits", related to each digit in a series, for example, the number 213 that we use in our daily life actually corresponds to 213 _{10.}

However, in addition to typing 10 digits (0 through 9), the decimal number system also has aggregation ( + ), subtraction ( – ), multiplication ( × ) and division (÷).

In a decimal system, each digit has a value ten times greater than the previous number, and this decimal number system uses a base, a series of symbols (b) together with q, to determine the weight of each digit within a number.

Any numbering system can be summarized with the following relationship:

N = b_{i} q^{i}

Where: N is a real positive number

b digit is base value q ( i )

integer can be positive, negative, or zero

N = b_{n} q^{n}… b_{3} q^{3} + b_{2} q^{2} + b_{1} q^{1} + b_{0} q^{0} + b_{-1} q^{-1} + b_{-2} q^{-2.}

## Tennk Number System

In the decimal, base-10, or decimal numbering system, each integer column contains units, decimals, hundred, thousands, and so on as you move from right to left along the number.Mathematically, these values are written as ^{10 0} , ^{10 1} , ^{10 2} , ^{10 3,} etc. Each position to the left of the decolon then indicates the increasing positive strength of 10. Likewise, for fractions, the weight of the number is more negative. As you move from left to right, there is a reduction in the value of ^{10} ^{-1} , 10 ^{-2 , 10 -3} etc.

Thus, we can see that the "dexer number system" has a base of *10 or modulo-10* (sometimes called MOD-10), and the position of each digit in the de de-dex system indicates the size or weight of that digit, which equals q.

The value of any decimal number will be equal to the sum of its digits multiplied by their corresponding weight.For example: N = 6163 _{10} (Six Thousand Hundred and Sixty-Three) is dexged to:

6000 + 100 + 60 + 3 = 6163

or the weight of each step can be written by reflecting:

( 6×1000 ) + ( 1×100 ) + ( 6×10 ) + ( 3×1 ) = 6163

or polynomial format can be written as follows:

( 6×10 ^{3} ) + ( 1×10 ^{2} ) + ( 6×10 ^{1} ) + ( 3×10 ^{0} ) = 6163

In this decimal numbering system example, the leftmost digit is the most meaningful digit or MSD, and the rightmost digit is the least meaningful digit or LSD.In other words, the number 6 is MSD because its leftmost position carries the most weight, and the number 3 is LSD because its position on the far right carries the least weight.

## Binary Number System

The binary number system is the most basic numbering system of all digital and computer-based systems, and the rules as binary numbers de-degering system are the same.However, unlike the de-depreding system that uses the forces of ten, the binary numbering system works on the forces of two and converts from base-2 to base-10 binary to de-de-depresing.

Digital logic and computer systems use only two values or states to represent a condition, a logic level of "1" or a logic level of "0", and each "0" and "1" are considered a single digit on a Basis.

In the binary number system, a binary number, such as 101100101, is expressed by the array " 1s " and " 0s ", and each right-to-left digit throughout the array has a value of twice as many as the previous digit.However, because it is a binary number, it can only have a value of "1" or "0", so q equals "2" (0 or 1), whose position indicates its weight in the string.

Because de deprectation is a weighted number, converting from de decisimal to binary number (base 10 to base 2) will also produce a weighted binary number where the rightmost bit is **Least Important Bit** or **LSB** and the bit on the left is the most. **The Most Important Bit** or **MSB** is represented in this way:

We saw above that in the de dexer number system, the weight of each step from right to left increases 10 times. As shown in the binary number system, the weight of each step increases by 2 times.

For example, if we want to convert a Binary to **a Deger,** here's what happens:

Decimal Place Value | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

Binary Digit Value | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |

If we combine all delusional values from right to left in the positions represented by " 1 ", it gives us the following value: (256) + (64) + (32) + (4) + (1) = 357 _{10} .

Then, we can convert the binary to a decimal number by finding the decimal equivalent of 101100101 _{2} binary digit arrays and extending the binary digits to a 2-based array that returns the equivalent of 357 _{10} in decimal or decimal.

Note that in number conversion systems, the "base" is used to specify the corresponding basic numbering system, _{1001 2 = 9 10.} _{}If a subscript is not used after a number, it is usually assumed to be a deity.

## Split-In-Two Method

Above we saw how to convert binary numbers to decimal numbers, but how do we convert a decimal number to a binary number?An easy way to convert a deger of deities to binary number equivalents is to write the de degerile number and continuously divide it by 2 (two) to continue until a result and the final result is "1" or "0" until the rest.

I mean, like.Let's convert the number 294 _{10} degers to binary number equivalent:

Count= | 294 | Dividing each deacted number by "2" returns one result plus the remainder. If the divided depreant number is even, the result is complete and equals the remaining "0".If the de deger is odd, the result is not fully divided and the remaining number is "1". The binary result is achieved by sorting all the remaining, with the least meaningful bit (LSB) at the top and the most meaningful bit (MSB) at the bottom. | |

Divide by 2 | |||

result | 147 | remaining | 0 (LSB) |

Divide by 2 | |||

result | 73 | remaining | 1 |

Divide by 2 | |||

result | 36 | remaining | 1 |

Divide by 2 | |||

result | 18 | remaining | 0 |

Divide by 2 | |||

result | 9 | remaining | 0 |

Divide by 2 | |||

result | 4 | remaining | 1 |

Divide by 2 | |||

result | 2 | remaining | 0 |

Divide by 2 | |||

result | 1 | remaining | 0 |

Divide by 2 | |||

result | 0 | remaining | 1 (MSB) |

This 2-to-2 split de-deger technique gives 294 _{10} degers the equivalent of_{2} 100100110 in pairs, reading from right to left.This 2-by-2 splitting method will also work for conversion to other number bases.

Next, we can see that the main characteristics of a binary number system are that each "binary digit" or "bit" has a value of "1" or "0", with each bit having twice the weight or value of the previous bit. Starting with the lowest or least meaningful bit (LSB), this is called the "sum of weights" method.

Thus, using the sum of weights method or using the method of dividing it by repeated 2, we can convert a decathlete number to a binary number and convert the binary to a decathlete number by finding the sum of the weights.

## Binary Number System and Pre-appendixes

Binary numbers can be aggregated and subtracted together, just like de deferment numbers; the result is combined into one of several dimension ranges, depending on the number of bits used.Binary numbers come in three basic formats – one bit, one byte, and one word, where bits are a single binary digit, one byte is eight binary digits, and one word is 16 binary digits.

The classification of individual lice in larger groups is often referred to by the following more common names:

Binary Digits (bits) | Common name |

1 | Louse |

4 | Nibble |

8 | Byte |

16 | Word |

32 | Double Word |

64 | Quad Word |

One way to overcome this problem when converting a binary number to de decathlete numbers and determine whether the numbers or numbers used are decathlete or binary numbers is to type a small number called "base" after the last digit to indicate the base of the number system.

For example, if we were using a binary array of numbers, we would add the sub-symbol "2" to indicate the base-2 number, so that the number is written as_{10 2.}Similarly, if there was a standard dex dexer number, we would add the subscript "10" to indicate a number based on 10, so that the number would be written as_{10 10.}

Microcontrollcular or microprocessor systems have become increasingly large. Bytes(bytes) in groups of 8 to create residing numbers instead of the corresponding binary digits (bits) are commonly sized, for example, most computer hardware used for hard disk and memory modules; size is represented by concepts such as megabytes or gigabytes.

Bytes | Common name |

1.024 (2 ^{10} ) | kilobytes (kb) |

1,048,576 (2 ^{20)} | Megabytes (Mb) |

1.073.741.824 (2 ^{30} ) | Gigabytes (Gb) |

That's a long number!(2 ^{40} ) | Terabytes (Tb) |

## Summarize

- " BIT " is an abbreviated term derived from BI nary digi T.
- A Binary system has only two state, Logic "0" and Logic "1", which returns the base of 2.
- A Decimal system uses 10 different digits, giving a base of 0 to 9 to 10.
- A binary number is a weighted number whose weighted value increases from right to left.
- The weight of a binary step doubles from right to left
- A deger can be converted to a binary number using the sum of weights method or repeated 2-by-2 split method.
- When we convert numbers from binary to decimal or decimal to binary, inscriptions are used to prevent errors.

Converting a binary number from a de deger (base-2 to base-10) or a degeri number from binary numbers (base10 to base-2) can be done in several different ways, as shown above.When converting decathlete numbers to binary numbers, it is important to remember which is the least meaningful bit ( LSB ) and which is the most meaningful bit (MSB).

In the next lesson on Binary Logic, we will examine converting binary numbers **to Hexadecimal Numbers** and vice versa, and show that binary numbers can be represented in letters as well as numbers.