The binary number system is one of the four types of number systems. In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1 (one). Here binary numbers are expressed in base-2 numeral system. For example, (101)2 is a binary number. Each digit in this system is called a bit.
Binary Number System
Binary is a number system created using the numbers 0 and 1. The binary number system has very important uses in writing computer programs and getting the computer to work. Because computer is an electrical device and current has only 2 results. Current on, or current off, according to the condition of this current, there are only 2 numbers in the binary number system. On current means 1, off current means 0. But these 2 numbers or current status cannot be used much directly. That's why a group of bits or binary numbers are used, according to which computer architects are made.
Like other number systems, in the binary number system, the face value and the place value are different, and as in the normal use decimal number system, the place value of the next position is multiplied by 10, like - 1000 is taking four places. To increase the number by one place or length, 1000 x10 = 10000 is done. Similarly, in binary number system, the value of the next position is multiplied by the value of the previous position by 2. For example - binary (100)2 of 4 is taking three places, in this, binary (1000)2 of 4x2 = 8 is done to extract the next place value by increasing one place or number length.
That is, each position in which a digit is written has a different position value. Each position is a power of the base, which is 2 for the binary number system, and these powers start at 0 and increase by 1.
Convert decimal number to binary. eg binary of 5 = (101)
In the decimal number system, we form numbers using the digits from 0-9. However, in the binary number system, we use only two digits, such as 0 and 1.
Now, let us discuss how to convert the decimal number 5 into binary number system.
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First, divide the number 5 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Continue this step until the quotient becomes 0.
Dividend Remainder 5/2= 2 1 2/2= 1 0 1/2= 0 1 -
Now, write the remainder in reverse chronological order. (ie from bottom to top).
binary of (5)10 = (101)2 है.
If we want to know how many bits are there in 5 in binary? We have to count the number of zeros and ones. So 5 = (101) in binary. Here 1 is zero and 2 is one. Therefore, the length and number of bits in 5 are 3.
How to find place value in binary number system.
To get the place value in the binary number system, subtract 1 from that place and raise it to the power of 2. In any number system, the counting of numbers starts from the last place.
For example - in binary (1000) the position value of one or place 4 will be .
(24-1 Or 2 3) Or (2x2x2) = (16)
binary number position value table (8 bit)
The following table shows the place values for an 8-bit binary number where all bits are on.
| bit value | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
|---|---|---|---|---|---|---|---|---|
| place value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| bit number | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
The value of a binary number is based on the presence of 1 bits and their positional values. So, the value of the given binary number is – 1 + 2 + 4 + 8 +16 + 32 + 64 + 128 = 255. Which is the same as 28-1.
Convert binary to decimal number. Like (1100)'s decimal = (12)
To convert a binary number to decimal, the place values of the bit position which is 1 are added.
To convert binary (1100)2 to decimal find the value of 1 at bit position -
24-1 = 8 ,23-1 = 4
add these values 8+4 = 12
That is, 1100 is a 4 bit binary number whose decimal value is 12.
how to count binary numbers
The decimal number system operates in base 10, with the digits 0–9 representing the numbers. The binary system operates in base 2 and the digits 0-1 represent numbers, and the base is known as the radix. Put differently, the above table can also be shown in the following way.
| Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|
| Decimal | 103 = 1000 | 102 = 100 | 101 = 10 | 100 = 1 |
| Binary | 23 = 8 | 22 = 4 | 21 = 2 | 20 = 1 |
Finding the value after a point in a binary number system. eg - 1001.110 = 9.75
Solution 23×1 + 22×0 + 21×0 + 20×1.21/2×1 +21/3×1 +21/4×0 = 9.75
To show values less than one, numbers may be placed to the right of the dot.
For 10.1, 10 is a whole number to the left of the decimal point, and the number place becomes larger as we move further to the left.
The first digit to the right is always ½ and the number gets smaller as we move more to the right.
"10" represents '2' in decimal. ".1" represents 'half'. So, "10.1" in binary is 2.5 in decimal.
Binary Arithmetic Operations - Addition Subtraction Multiplication Division
We can perform the operations of addition, subtraction, multiplication and division on binary numbers just as we perform arithmetic operations on numbers. Let us know them one by one.
For example: add 1001 and 1001.
1001 +1011 _______ =10100
For example: Subtract 1101 and 1010.
1101
-1010
______
=0011
For example: multiply 1101 and 1010.
1101
x 1011
_______
0000
1101x
0000xx
1101xxx
________
10000010
For example: divide 1010 by 10.
10)1010(101
10
010
10
0
- Binary numbers are made up of only 0 and 1.
- A binary number is represented in base-2 (10110)2
Binary Numbers Table
| Decimal number | Binary number | Decimal number | Binary number |
|---|---|---|---|
| 1 | 1 | 11 | 1011 |
| 2 | 10 | 12 | 1100 |
| 3 | 11 | 13 | 1101 |
| 4 | 100 | 14 | 1110 |
| 5 | 101 | 15 | 1111 |
| 6 | 110 | 16 | 10000 |
| 7 | 111 | 17 | 10001 |
| 8 | 1000 | 18 | 10010 |
| 9 | 1001 | 19 | 10011 |
| 10 | 1010 | 20 | 10100 |
What is binary number system?
A number system where a number is represented using only two digits (0 and 1) with base 2 is called binary number system. For example, 1001 is a binary number.
What is bit?
A bit is a digit in a binary number. For example, 101 is a three-bit binary number, where 1, 0, and 1 are bits.
What is the use of binary number?
Binary numbers are commonly used in computer architecture. Since the computer only understands the language of two digits 0 and 1, programming is done using the binary number system.
