Number System

The Number System is the collection of discrete symbols of numbers used to represent the quantity of any elements. For Example, the number system we follow in the Real world is the Decimal number system, also known as the Base 10 number system. Which means that there are 10 different discrete symbols are used to represent the quantity. Those 10 discrete symbols are 0,1,2,3,4,5,6,7,8,9. This number system is also known as Decimal Number System. Whatever number we consider, it only consists of only these 10 symbols. And there are other types of number systems also. For example Base2, Base8, and Base16. These are the 4 types of number systems we generally follow. In Base2 number system, we only have two unique symbols : 0 and 1. This number system is also known as Binary Number System. In Base8 number system, we only have 8 unique symbols: 0,1,2,3,4,5,6 and 7. This number system is also known as Octal Number System. In Base16 number system, we only have 16 unique symbols: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F. This number system is also known as Hexadecimal Number System.

Even though we have these many number systems, they all are used to represent the unique quantity. Let’s look at their equivalent representation for different numbers.

Even though 1100 means One thousand One hundred in the Decimal system, it is only twelve in Binary. Out of these 4 number systems, we generally use the Decimal number system in the real world. Why? Because we have been told about that number system only from our childhood. So, everyone got used to it. Are these the only number systems we have? No. We can form our own number systems by changing the base value. We can form Base5 number system by making the base 5 with only 5 unique symbols. In every number system, the count gets increased by wrapping at the end symbol and placing the next highest symbol to the left.

Out of these all number system, why Binary number system is considered for the Digital Computation? Because it only has two unique symbols to represent any number. These two symbols can be practically implemented as ON, OFF of a switch. Generally, 0 represents OFF and 1 represents ON. So, any number from any number system has to be converted to the binary number system to use it in the digital computations. The Rightmost bit is known as Least Significant Bit (LSB) and the leftmost bit is known as Most Significant Bit (MSB). Let’s look at the conversions of the numbers between these major 4 number systems.

Decimal to Others

Decimal to Binary:

Decimal to binary conversion can be done by continuously taking the remainders of division of the decimal number by 2 from bottom to top till the quotient becomes 0.

Decimal 56:

By taking the remainders from bottom to top, binary 111000 represents 56.

Decimal 29:

By taking the remainders from bottom to top, binary 11101 represents 29.

Decimal to Octal:

Decimal to Octal conversion can be done by continuously taking the remainders of division of the decimal number by 8 from bottom to top till the quotient becomes 0.

Decimal 56:

By taking the remainders from bottom to top, Octal 70 represents 56.

Decimal 29:

By taking the remainders from bottom to top, Octal 35 represents 29.

Decimal to Hexadecimal:

Decimal to Hexadecimal conversion can be done by continuously taking the remainders of division of the decimal number by 16 from bottom to top till the quotient becomes 0.

Decimal 56:

By taking the remainders from bottom to top, Hexadecimal 38 represents 56.

Decimal 29:

By taking the remainders from bottom to top, Hexadecimal 1D represents 29.

Hexadecimal to Others

Hexadecimal to Binary:

Hexadecimal to Binary conversion can be done by directly writing the equivalent binary representation of each of the Hexadecimal symbol and concatenate them.

Hexadecimal D5:

The binary representation of D5 is 11010101.

Hexadecimal 83A:

The binary representation of 83A is 100000111010.

Hexadecimal to Octal:

Hexadecimal to Octal conversion can be done by three steps: 1) First convert Hexadecimal into Binary. 2) Conver the binary into Octal. To Convert the binary into Octal, divide the binary into the groups of 3 bits from the right side. If the 3 bits are not available for the leftmost group, pad 0’s. 3) Write the Octal equivalent for each group of binary numbers.

Hexadecimal D5:

The binary representation of D5 is 11010101.

The Octal representation of D5 is 325.

Hexadecimal 83A:

The binary representation of 83A is 100000111010.

The Octal representation of 83A is 4072.

Hexadecimal to Decimal:

Hexadecimal to Decimal conversion can be done by summation of the multiplication of each digit with 16 powered digit weight. The Digit weight of the rightmost digit is 0.

Hexadecimal D5:

The Decimal representation of D5 is 213.

Hexadecimal 83A:

The Decimal representation of 83A is 2106.

Octal to Others

Octal to Hexadecimal

Octal to Hexadecimal conversion can be done by first converting octal to binary and then grouping the binary of 4 bits from right. Pad 0’s for the rightmost group if 4 bits are not available. And write the Hexadecimal Equivalent for each group.

Octal 65:

The Hexadecimal representation of 65 is 35.

Octal 346:

The Hexadecimal representation of 346 is E6.

Octal to Decimal

Octal to Decimal conversion can be done by summation of the multiplication of each digit with 8 powered digit weight. The Digit weight of the rightmost digit is 0.

Octal 65:

The Hexadecimal representation of 65 is 53.

Octal 346:

The Hexadecimal representation of 346 is 230.

Octal to Binary

Octal to Binary conversion can be done by writing the binary equivalent for each digit of Octal.

Octal 65:

The Hexadecimal representation of 65 is 110101.

Octal 346:

The Hexadecimal representation of 346 is 011100110.

Binary to Others

Binary to Hexadecimal

Binary to Hexadecimal conversion can be done by writing the binary digits into the groups of 4 bits and writing equivalent Hexadecimal value for each group.

Binary 11000111:

The Hexadecimal representation of 11000111 is C7.

Binary 10101:

The Hexadecimal representation of 11000111 is 15.

Binary to Decimal

Binary to Decimal conversion can be done by summation of the multiplication of each digit with 2 powered digit weight.The Digit weight of the rightmost digit is 0.

Binary 11000111: