1023 in Binary
1023 = 1111111111₂
The decimal number 1023 is 11 1111 1111 in binary.
Step by step
- 1023 ÷ 2 = 511 remainder 1
- 511 ÷ 2 = 255 remainder 1
- 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
- Read the remainders from bottom to top: 1111111111.
Check the answer by adding the place values: 1×512 + 1×256 + 1×128 + 1×64 + 1×32 + 1×16 + 1×8 + 1×4 + 1×2 + 1×1 = 1,023. Each 1 bit adds its power of two and each 0 bit adds nothing.
Details
- Binary
- 11 1111 1111
- 8-bit form
- Needs 10 bits
- Hexadecimal
- 3FF
- Octal
- 1777
- Bits needed
- 10
- Number of 1 bits
- 10
How it works
Binary is base 2: each digit is a bit worth a power of two (1, 2, 4, 8, 16, 32 …). To convert a decimal number to binary, divide it by 2 again and again, writing down each remainder (0 or 1), until the quotient reaches 0. The binary number is the remainders read from the last one to the first. To check, add the powers of two where the bits are 1.
Nearby values
Related conversions
Frequently asked questions
What is 1023 in binary?
1111111111.
How do you convert 1023 to binary?
Divide by 2 repeatedly and read the remainders from bottom to top.
How many bits are needed for 1023?
10 bits.
What is 1023 in hexadecimal?
3FF.