Use our Base converter calculator to learn Number base conversion within various base systems including, Binary, Ternary, Octal, Decimal and Hexadecimal. Using this Number System calculator with solution to know detailed steps for Decimal to Binary conversion, Decimal to Hex conversion, Decimal to Octal conversion, Binary to Decimal conversion, Binary to Hex conversion, Binary to Octal conversion, Octal to Binary conversion, Octal to Decimal conversion, Octal to Hex conversion, Hex to Binary conversion, Hex to Octal conversion, Hex to Decimal conversion and many more.

What Number System?

A numeral system is a writing system for expressing numbers. For example “11” is used to represent number 11 (Eleven) in decimal numeral system while it’s used to represent number 3 (three) in binary numeral system.

The most commonly used system of numerals is decimal which is based on the Hindu–Arabic numeral system. Indian mathematicians developed the concept of Place value system and the number Zero. In any number system each digit has a value and position.

So numeral a_na_{n − 1}a_{n − 2} … a₀in numeral system b means a_nbⁿa_{n − 1}b^n-1a_{n − 2}b^n-2 … a₀b⁰

For example, in the decimal system (base 10), the numeral 5347 means (5×10³) + (3×10²) + (4×10¹) + (7×10⁰)

Also in any number system Most Significant Bit (MSB) is the bit on the far left end of the number, while the Least Significant Bit (LSB) is the bit on the far right end (LSB).

Popular Number Base Systems

Base	Name	Number of Numerals	Symbols
2	Binary	2	0, 1
3	Ternary	3	0, 1, 2
5	Quinary (Pental)	5	0, 1, 2, 3, 4
8	Octal	8	0, 1, 2, 3, 4, 5, 6, 7
10	Decimal	10	0, 1, 2, 3, 4, 5, 6, 7, 8, 9
16	Hexadecimal	16	0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

How to Convert from Decimal to Other Bases

There are various direct or indirect methods to convert a decimal number into other number systems.

Decimal to Binary Conversion – How to Convert Decimal to Binary?

Method 1 Decimal to Binary Conversion using the Division by 2 with Remainder

To convert the numbers from decimal to binary, follow the below conversion steps

Take the Decimal Number
Divide this number by 2 (as we are converting to base 2)
Note down the remainder
Now divide the quotient by 2 and store the remainder
Repeat the above steps until you get 0 as the quotient
Now writing these remainders from MSB (bottommost remainder) to LSB (topmost remainder) the required binary number can be obtained.

Let’s convert 156 from base 10 to base 2 using this method

	Quotient	Remainder
156/2	78	0
78/2	39	0
39/2	19	1
19/2	9	1
9/2	4	1
4/2	2	0
2/2	1	0
1/2	0	1

So number 156 in base 2 = 10011100

Method 2: Descending Powers of 2 and Subtraction

To convert the numbers from decimal to binary, follow the below conversion steps

List the powers of 2 until you reach the number closet to the decimal number (Z) which needs to be converted to binary
Identify the greatest power of 2 from this list
Write 1 beneath this power of 2, Subtract the above from the decimal number Z to get the new number
Move to the next lower power of 2, Check if this power of 2 is greater than the new number
1. if yes write 0 below this power of 2 and move to the next power
2. if no write 1 beneath this power of 2, Subtract the above from the new number to get another new number
Continue untill you reach the lowest power of 2 (2⁰)
Number in binary will be same left to right the number mentioned beneath each power

Let’s convert 156 from base 10 to base 2.

	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
Z=156	128	64	32	16	8	4	2	1
Factor	1	0	0	1	1	1	0	0
Number after subtraction	156-128=28			12	4	0

So number 156 in base 2 = 10011100

Decimal to Octal Conversion – How to Convert Decimal to Octal?

Method 1 Decimal to Octal Conversion using the Division by 8 with Remainder

To convert the numbers from decimal to octal, follow the below conversion steps

Take the Decimal Number
Divide this number by 8 (as we are converting to base 8)
Note down the remainder
Now divide the quotient by 8 and store the remainder
Repeat the above steps until you get 0 as the quotient
Now writing these remainders from MSB (bottommost remainder) to LSB (topmost remainder) the required binary number can be obtained.

Let’s convert 156 from base 10 to base 8 using this method.

	Quotient	Remainder
156/8	19	4
19/8	2	3
2/8	0	2

So number 156 in base 8 = 234

Method 2: Descending Powers of 8 and Subtraction

To convert the numbers from decimal to binary, follow the below conversion steps

List the powers of 8 until you reach the number closet to the decimal number (Z) which needs to be converted to binary
Identify the greatest power of 8 from this list
Write 1 beneath this power of 8, Subtract the above from the decimal number Z to get the new number
Move to the next lower power of 8, Check if this power of 8 is greater than the new number
1. if yes write 0 below this power of 8 and move to the next power
2. if no write 1 beneath this power of 8, Subtract the above from the new number to get another new number
Continue untill you reach the lowest power of 8 (8⁰)
Number in binary will be same left to right the number mentioned beneath each power

Let’s convert 156 from base 10 to base 8.

	8³	8²	8¹	8⁰
Z=156	512	64	8	1
Factor		2	3	4
Number after subtraction (remainder)		156-64=28	28-24=4	4-4=0

So number 156 in base 8 = 234

Decimal to Hexadecimal Conversion – How to Convert Decimal to Hexadecimal?

Method 1 Decimal to Hexadecimal Conversion using the Division by 16 with Remainder

To convert the numbers from decimal to hexadecimal, follow the below conversion steps

Take the Decimal Number
Divide this number by 16 (as we are converting to base 16)
Note down the remainder
Now divide the quotient by 16 and store the remainder
Repeat the above steps until you get 0 as the quotient
Now writing these remainders from MSB (bottommost remainder) to LSB (topmost remainder) the required binary number can be obtained.

Let’s convert 554 from base 10 to base 16 using this method.

	Quotient	Remainder
554/16	34	10 (10 in base-16 is A)
34/16	2	2
2/16	0	2

So number 554 in base 16 = 22A

Method 2: Descending Powers of 16 and Subtraction

To convert the numbers from decimal to hexadecimal, follow the below conversion steps

List the powers of 16 until you reach the number closet to the decimal number (Z) which needs to be converted to binary
Identify the greatest power of 16 from this list
Write 1 beneath this power of 16, Subtract the above from the decimal number Z to get the new number
Move to the next lower power of 16, Check if this power of 16 is greater than the new number
1. if yes write 0 below this power of 16 and move to the next power
2. if no write 1 beneath this power of 16, Subtract the above from the new number to get another new number
Continue untill you reach the lowest power of 16 (16⁰)
Number in binary will be same left to right the number mentioned beneath each power

Let’s convert 554 from base 10 to base 16.

	16³	16²	16¹	16⁰
Z=554	4096	256	16	1
Factor		2	2	10 (10 in base-16 is A)
Number after subtraction (remainder)		554-512=42	42-32=10	10-10=0

So number 554 in base 16 = 22A

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