Number Base Converter

Convert between decimal, binary, hexadecimal, octal and other number systems with step-by-step solutions.

From

Valid digits: 0123456789

255 (Base 10) = 11111111 (Base 2)

Step-by-Step Solution

1Convert Decimal to Binary:

Repeatedly divide by 2 and collect remainders (read bottom to top):

Step	Dividend	÷ 2	Quotient	Remainder	Digit
1	255	÷ 2	127	1	1
2	127	÷ 2	63	1	1
3	63	÷ 2	31	1	1
4	31	÷ 2	15	1	1
5	15	÷ 2	7	1	1
6	7	÷ 2	3	1	1
7	3	÷ 2	1	1	1
8	1	÷ 2	0	1	1

Reading remainders bottom to top: 11111111

2Result:

255 (Base 10) = 11111111 (Base 2)

View Decimal to Binary page →

255 (Base 10) in All Bases

Number System	Base	Value
Binary	2	11111111
Octal	8	377
Hexadecimal	16	FF
Ternary	3	100110
Quaternary	4	3333
Quinary	5	2010
Senary	6	1103
Septenary	7	513
Duodecimal	12	193
Vigesimal	20	CF
Duotrigesimal	32	7V
Hexatrigesimal	36	73

Common Values in Different Bases

Decimal	Decimal	Binary
0	0	0
1	1	1
2	2	10
3	3	11
4	4	100
5	5	101
6	6	110
7	7	111
8	8	1000
9	9	1001
10	10	1010
15	15	1111
16	16	10000
20	20	10100
32	32	100000

Number System Reference

Name	Base	Digits	Description
Binary	2	01	Used in computers and digital systems
Octal	8	01234567	Used in Unix file permissions
Decimal	10	0123456789	Standard number system
Hexadecimal	16	0123456789ABCDEF	Used in programming and colors
Ternary	3	012	Three-valued logic
Quaternary	4	0123	Used in DNA encoding
Quinary	5	01234	Based on counting fingers on one hand
Senary	6	012345	Highest 1-digit prime base
Septenary	7	0123456	Days of the week
Duodecimal	12	0123456789AB	Dozen system, highly divisible
Vigesimal	20	0123456789ABCDEFGHIJ	Maya numeral system
Duotrigesimal	32	0123456789ABCDEFGHIJKLMNOPQRSTUV	Used in encoding schemes
Hexatrigesimal	36	0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ	Uses all alphanumeric characters

Popular Conversions

Decimal to Binary Binary to Decimal Decimal to Hexadecimal Hexadecimal to Decimal Decimal to Octal Octal to Decimal Binary to Hexadecimal Hexadecimal to Binary Binary to Octal Octal to Binary Decimal to Duodecimal Decimal to Ternary

How Number Base Conversion Works

A number base (or radix) determines how many unique digits are used to represent numbers. The decimal system uses 10 digits (0-9), binary uses 2 (0-1), and hexadecimal uses 16 (0-9, A-F).

Converting to Decimal

Each digit is multiplied by the base raised to its position power. For example, binary 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 in decimal.

Converting from Decimal

Repeatedly divide by the target base and collect remainders. Read the remainders from bottom to top to get the result. For example, 11 ÷ 2 gives remainders 1,1,0,1 → 1011 in binary.

Common Number Systems

Binary (Base 2) - Used in computers; only 0s and 1s
Octal (Base 8) - Used in Unix file permissions
Decimal (Base 10) - Standard human counting system
Hexadecimal (Base 16) - Used in programming, colors (e.g., #FF5733)
Duodecimal (Base 12) - Historical system, highly divisible