Digital computer represents all kinds of data and information in the binary system. Binary Number System consists of two digits 0 and 1. Its base is 2. Each digit or bit in binary number system can be 0 or 1. A combination of binary numbers may be used to represent different quantities like 1001. The positional value of each digit in binary number is twice the place value or face value of the digit of its right side. The weight of each position is a power of 2.
The place value of the digits according to position and weight is as follows:
Position
3
2
1
0
Weights
23
22
21
20
Example: Convert 101112 decimal number
Position
2
1
0
-1
-2
Weights
102
101
100
10-1
10-2
Face Value
1
3
9
7
8
101112 = 1 x 24 + 0 x 23 + 1 x 22 + 1 x 21 + 1 x 20
= 1 x 16 + 0 + 1 x 4 + 1 x 2 + 1 x 1
= 16 + 0 + 4 2 + 1
= 2310
Decimal number system
The Decimal Number System consists of ten digits from 0 to 9. These digits can be used to represent any numeric value. The base of decimal number system is 10. It is the most widely used number system. The value represented by individual digit depends on weight and position of the digit.
Each number in this system consists of digits which are located at different positions. The position of first digit towards left side of the decimal point is 0. The position of second digit towards left side of the decimal point is 1. Similarly, the position of first digit towards right side of decimal point is -1. The position of second digit towards right side of decimal point is -2 and so on.
The value of the number is determined by multiplying the digits with the weight of their position and adding the results. This method is known as expansion method. The rightmost digit of number has the lowest weight. This digit is called Least Significant Digit (LSD). The leftmost digit of a number has the highest weight. This digit is called Most Significant Digit (MSD). The digit 7 in the number 724 is most significant digit and 4 is the least significant digit.
Decimal to binary conversion examples
(51)10 = (110011)2
(217)10 = (11011001)2
(8023)10 = (1111101010111)2
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The binary number system is a numeral system that represents numbers using two symbols: 0 and 1. It is the base-2 numeral system, and the number 2 is called the base. The binary numeral system is used in digital electronics, computer science, and many other fields.
The decimal number system is the most common numeral system in use today. It is a base-10 numeral system, and the number 10 is called the base. The decimal numeral system is used in everyday life for counting, measuring, and calculating.
To convert a binary number to a decimal number, you can use the following steps:
Write down the binary number.
Starting from the right, multiply each digit in the binary number by 2 raised to the power of its position.
Add the products together.
For example, to convert the binary number 1011 to decimal, you would do the following:
Write down the binary number: 1011
Starting from the right, multiply each digit in the binary number by 2 raised to the power of its position:
1 x 2^3 = 8
0 x 2^2 = 0
1 x 2^1 = 2
1 x 2^0 = 1
Add the products together: 8 + 0 + 2 + 1 = 11
Therefore, the decimal equivalent of the binary number 1011 is 11.
To convert a decimal number to a binary number, you can use the following steps:
Divide the decimal number by 2.
Write down the remainder.
If the quotient is not 0, go back to step 1.
For example, to convert the decimal number 11 to binary, you would do the following:
Divide 11 by 2: 11 / 2 = 5, remainder 1
Write down the remainder: 1
The quotient is 5, which is not 0, so go back to step 1.
Divide 5 by 2: 5 / 2 = 2, remainder 1
Write down the remainder: 1
The quotient is 2, which is not 0, so go back to step 1.
Divide 2 by 2: 2 / 2 = 1, remainder 0
The quotient is 1, which is 0, so stop.
The remainders you have written down are 1, 1, and 0. This is the binary representation of the decimal number 11.
Binary addition is the process of adding two binary numbers together. To add two binary numbers, you can use the following steps:
Line up the binary numbers so that the corresponding digits are in the same column.
Starting from the right, add the digits in each column.
If the sum of the digits in a column is greater than 1, carry the 1 over to the next column.
Continue adding the digits in each column, carrying over as necessary.
The sum of the two binary numbers is the number you have written down.
For example, to add the binary numbers 1011 and 1101, you would do the following:
Line up the binary numbers so that the corresponding digits are in the same column:
1011
1101
Starting from the right, add the digits in each column:
1 + 1 = 10
0 + 1 + 1 = 10
1 + 0 + 0 = 1
1 + 1 + 1 = 11
Since the sum of the digits in the third column is greater than 1, carry the 1 over to the next column:
10
11
1
Continue adding the digits in each column, carrying over as necessary:
10
11
1
1
1010
The sum of the two binary numbers is 1010.
Binary subtraction is the process of subtracting two binary numbers. To subtract two binary numbers, you can use the following steps:
Line up the binary numbers so that the corresponding digits are in the same column.
Starting from the right, subtract the digits
What is a binary number?
A binary number is a number that is represented using only two digits: 0 and 1. It is a base-2 number system, which means that each digit position has a value that is a power of 2. The rightmost digit position has a value of 2^0, the next digit position has a value of 2^1, and so on.
How do you convert a binary number to a decimal number?
To convert a binary number to a decimal number, you can use the following formula:
How do you convert a decimal number to a binary number?
To convert a decimal number to a binary number, you can use the following algorithm:
Divide the decimal number by 2.
Write down the remainder.
If the quotient is not 0, go back to step 1.
Starting from the bottom, write down the remainders in reverse order.
For example, to convert the decimal number 11 to a binary number, you would use the following algorithm:
11 / 2 = 5, remainder 1
5 / 2 = 2, remainder 1
2 / 2 = 1, remainder 0
1 / 2 = 0, remainder 1
The remainders in reverse order are 1, 1, 0, so the binary number is 110.
What is a hexadecimal number?
A hexadecimal number is a number that is represented using 16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. It is a base-16 number system, which means that each digit position has a value that is a power of 16. The rightmost digit position has a value of 16^0, the next digit position has a value of 16^1, and so on.
How do you convert a hexadecimal number to a decimal number?
To convert a hexadecimal number to a decimal number, you can use the following formula: