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# What is Binary Value? – Definition, Advantages, Converting, And More

## Binary Value – Definition

Binary Value is in mathematics binary number system, and the positional numeral system employs two as the base. It requires only two different symbols for its digits, 0 and 1, instead of the usual ten different symbols needed in the decimal system. The facts from 0 to 10 are thus in binary 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, and 1010. The importance of the binary system to data models and computer technology originates mainly from the solid and reliable manner in which 0s and 1s can be represented in electromechanical devices.

### A single binary digit is called a “Bit”. A binary number consists of several bits. Examples are:

• 10101 is a five-bit binary number
• 101 is a three-bit binary number
• 100001 is a six-bit binary number

## Binary Value System: Application & Advantages

‘There are ten kinds of people, those who understand binary and those who don’t. The most commonly used number system, called base-ten, uses ten digits: 0-9. By comparison, the binary number system, or base-two, is a counting technique that uses two digits: 0 and 1. Here, the prefix ‘bi’ means ‘two.’ If you don’t already understand why this is funny, you will by the end of this lesson.

In this system, each residence value is a power of two, where the first place to the left of the decimal point is 2^0, the second place is 2^1 and so on. Each number is called a bit and is pronounced separately. For example, when referring to this binary number:

## Converting Numbers from Binary Value to Decimal

If you give a number written in binary, you can translate it to a decimal by multiplying each binary bit by its power of two and adding all the results. For example, the binary number 11101 convert to decimal. Convert the binary number to her equivalent decimal number in the following criteria.

#### Examples of Binary Value

1001

10101

11000

##### Solutions of Binary Value

If 1001 we have (1 * (2^3)) + (0 * (2^2)) + (0*(2^1)) + (1*(2^0)) = 8 + 1 = 9

The 10101 we have (1 * (2^4)) + (0 * (2^3)) + (1 * (2^2)) + (0 * (2^1)) + (1 * (2^0)) = 16 + 4 + 1 = 21

For 11000 we have (1 * (2^4)) + (1 * (2^3)) + (0 * (2^2)) + (0 * (2^1)) + (0 * (2^0)) = 16 + 8 = 24

### Converting Numbers from Decimal to Binary Value

We can also convert numbers written in decimal to binary numbers. First, find the main power of 2 less than or equal to the decimal number. Find the difference between the original number and this power of 2. Then find the most significant power of 2 less than or equal to this new number. Repeat this process until you have no powers of 2 left. The decimal number is the sum of all the powers of 2 you found – to write the number in binary, put a 1 in for the bit representing each power of 2 you found, and a 0 in for all other bits.

For example, for the decimal number 29, the highest power of 2 that is less than or equal to 29 is 2^4 = 16. The difference between 29 and 16 is 13. The maximum influence of 2 less than or equivalent to 13 is 2^3 = 8. The difference between 13 and 8 is 5. The all-out power of 2 less than or like five is 2^2 = 4. The difference between 5 and 4 is 1. The highest power of 2 less than or equal to 1 is 2^0 = 1. This last difference is 0, so we are done. This means our decimal number of 29 writes, making the binary version of 29 the number 11101. In the following examples, convert the decimal number to binary.

#### Examples

19

33

##### Solutions

For 19, the highest power of 2 is 2^4 = 16. The difference is 3. The highest power of 2 for 3 is 2^1 = 2. The difference is 1. The last power of 2 needed is 2^0 = 1, and the last difference is 0. This means that the decimal number 19 write as (1*(2^4)) + (0*(2^3)) + (0*(2^2)) + (1*(2^1)) + (1*(2^0)) and so the binary version of 19 is 10011.

For 33, the highest power of 2 is two ^5 = 32. This means that the decimal number 33 write as (1*(2^0)); thus, the binary version of 33 is 100001.

## Subtracting Binary Numbers

The most common way of subtracting binary numbers is done by first taking the second value (the number to be subtracted) and applying what is known as two’s complement, this is done in two steps: complement each digit in turn (change 1 for 0 and 0 for 1). add 1 (one) to the result.

Note: The first step by itself is known as one’s complement.
By applying these steps you are effectively turning the value into a negative number, and as when dealing with decimal numbers, if you add a negative number to a positive number then you are effectively subtracting to the same value. In other words, 25 + (-8) = 17, which is the same as writing 25 – 8 = 17.
An example, let’s do the following subtraction 11101011 – 01100110 (23510 – 10210).

## Conclusion

The most common request for the binary number arrangement is computer technology. All computer languages and programming are based on the 2-digit number system used in the digital encoding. Digital encoding is taking data and representing it with discreet bits of information. These careful bits consist of the 0s and 1s of the binary system.

For example, the images you see on your computer screen consume prearrange with a binary line for each pixel. If a screen uses a 16-bit code, each pixel is told what colour to show based on which bits are 0s and 1s. As a result, 2^16 signifies 65,536 different colours! We also find the binary number system in a branch of mathematics known as Boolean algebra. Here, either true or false statements assign a 0 or 1. This field of mathematics is anxious with logic and truth values.

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