In the decimal number systems each of the ten digits, 0 through 9, represents a certain quantity. The position of each digit in a decimal number indicates the magnitude of the quantity represented and can be assigned a weight. The weights for whole numbers are positive powers of ten that increases from right to left, beginning with 10º = 1 that is 10³ 10² 10¹ 10º

For fractional numbers, the weights are negative powers of ten that decrease from left to right beginningwith 10¯¹ that is 10² 10¹ 10º. 10¯¹ 10¯² 10¯³

The value of a decimal number is the sum of digits after each digit has been multiplied by its weights asin following examples

**Ex****p****re****s****s the decimal number 87 as a sum of the values of each digit**.

The digit 8 has a weight of10 which is 10 as indicated by its position. The digit 7 has a weight of 1 which is 10º as indicated by its position.

**8****7 = (8 x 10****1****) ****+ (7 x 10****0****)**

**Ex****p****re****s****s the decimal number 725.45 as a sum of the values of each digit.**

**725****. 45 = (7 x 10²) + (2 x 10¹) + (5 x 10º) + (4 x 10¯¹) + (5 x 10¯²) = 700 + 20 + 5 + 0.4 + 0.05**

__BI____NAR____Y NUMBERS__

The binary system is less complicated than the decimal system because it has only two digits, it is a basetwo system. The two binary digits (bits) are 1 and 0. The position of a 1 or 0 in a binary number indicates its weight, or value within the number, just as the position of a decimal digit determines the value of that digit. The weights in a binary number are based on power of two as:

**….****. 2****4 ****2****³ 2****2 ****2****1 ****2****0****. 2****-****1 ****2****-****2 ****….**

With 4 digits position we can count from zero to 15.In general, with n bits we can count up to a number equal to Ķ - 1. Largest decimal number = Ķ - 1.A binary number is a weighted number. The right-most bit is the least significant bit (LSB) in a binary whole number and has a weight of

2º =1. The weights increase from right to left by a power of two for each bit. The left-most bit is the most significant bit (MSB); its weight depends on the size of the binary number.

__BI____NARY-____T____O____-D____E____C____I____M____A____L CONVERSION__

The decimal value of any binary number can be found by adding the weights of all bits that are 1 and discarding the weights of all bits that are 0

Example

Let‘s convert the binary whole number 101101 to decimal

**W****e****ig****h****t****:****2****5 ****2****4 ****2****3 ****2****2 ****2****1 ****2****0**

**X**

**Bin****a****r****y no: 1 0 1 1 0 1**

**Va****lu****e 32 0 8 4 0 1**

**S****u****m = 45**

Decimal numbers are essential mathematical concept it allows represent and work with fractional quantities. 10 Signs You Are New For Photography They precision in calculation from finance. Decimal numbers complex calculations, numerical number.

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