Decimal Converter
Convert decimal numbers (base-10) to binary, octal, hexadecimal, and any custom base. The most common number system used in everyday mathematics.
Decimal Number Converter
Convert decimal numbers (base-10) to binary, octal, hexadecimal, and any custom base.
Decimal (Base-10)
Only digits 0-9 are allowed
Result will appear here
Decimal to Binary Conversion
Conversion Method:
Decimal to Base 2: Use division method
Method:
Divide by target base, collect remainders from bottom to top
Examples with Step-by-Step Solutions
Example 1:
(255)10
=
(11111111)2
Step-by-Step Solution:
Converting 255₍10₎ to base 2:
Step 2: Convert decimal 255 to base 2
Divide by 2 repeatedly and collect remainders:
255 ÷ 2 = 127 remainder 1
127 ÷ 2 = 63 remainder 1
63 ÷ 2 = 31 remainder 1
31 ÷ 2 = 15 remainder 1
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top: 11111111₍2₎
Therefore: 255₍10₎ = 11111111₍2₎
Example 2:
(1024)10
=
(10000000000)2
Step-by-Step Solution:
Converting 1024₍10₎ to base 2:
Step 2: Convert decimal 1024 to base 2
Divide by 2 repeatedly and collect remainders:
1024 ÷ 2 = 512 remainder 0
512 ÷ 2 = 256 remainder 0
256 ÷ 2 = 128 remainder 0
128 ÷ 2 = 64 remainder 0
64 ÷ 2 = 32 remainder 0
32 ÷ 2 = 16 remainder 0
16 ÷ 2 = 8 remainder 0
8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top: 10000000000₍2₎
Therefore: 1024₍10₎ = 10000000000₍2₎
Example 3:
(999)10
=
(1111100111)2
Step-by-Step Solution:
Converting 999₍10₎ to base 2:
Step 2: Convert decimal 999 to base 2
Divide by 2 repeatedly and collect remainders:
999 ÷ 2 = 499 remainder 1
499 ÷ 2 = 249 remainder 1
249 ÷ 2 = 124 remainder 1
124 ÷ 2 = 62 remainder 0
62 ÷ 2 = 31 remainder 0
31 ÷ 2 = 15 remainder 1
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top: 1111100111₍2₎
Therefore: 999₍10₎ = 1111100111₍2₎
Example 4:
(512)10
=
(1000000000)2
Step-by-Step Solution:
Converting 512₍10₎ to base 2:
Step 2: Convert decimal 512 to base 2
Divide by 2 repeatedly and collect remainders:
512 ÷ 2 = 256 remainder 0
256 ÷ 2 = 128 remainder 0
128 ÷ 2 = 64 remainder 0
64 ÷ 2 = 32 remainder 0
32 ÷ 2 = 16 remainder 0
16 ÷ 2 = 8 remainder 0
8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top: 1000000000₍2₎
Therefore: 512₍10₎ = 1000000000₍2₎