0 in Binary
× 1
Zero is written as a single 0.
MODERN · BASE 2
Binary
Two digits, 0 and 1, count powers of two. Decimal 42 becomes 101010 in binary.
Convert numbers- Place
- Worldwide · digital computing
- Period / variant
- Modern computing; earlier mathematical roots
EXAMPLES
42 · Base 2
101010: 32 + 8 + 2 = 42.
Worked example
Write 42 in Binary
Read from left to right. The rightmost place counts ones; each place to its left is worth 2 times as much.
42 ÷ 32 = 1, remainder 10. Start with 1 in the 32s place, then write the remainder in the lower places.
- × 32
This sign is the digit 1. In the 32s place, it contributes 1 × 32 = 32.
- × 16
This sign is the digit 0. Keep zero in the 16s place; this position contributes nothing.
- × 8
10 ÷ 8 = 1, remainder 2. This sign is the digit 1. In the 8s place, it contributes 1 × 8 = 8.
- × 4
This sign is the digit 0. Keep zero in the 4s place; this position contributes nothing.
- × 2
2 ÷ 2 = 1, remainder 0. This sign is the digit 1. In the 2s place, it contributes 1 × 2 = 2.
- × 1
This sign is the digit 0. Keep zero in the ones place; this position contributes nothing.
Check
1 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 1 × 2 + 0 = 42
Meet the symbols
Each tile shows one digit and its value. These are the 2 digits used by this display. Combine them using the rules below.
- 0
- 1
How the symbols fit together
Read from left to right, using only 0 and 1. From the right, the places are worth 1, 2, 4, 8, 16, 32, and so on. Add the places that contain a 1.
- There are two digits: 0 and 1. Each position to the left is worth twice as much as the previous one.
- For 101010, label the places from left to right: 32, 16, 8, 4, 2, 1.
- The 1 digits contribute 32, 8, and 2. The 0 digits keep the other positions empty.
- Add 32 + 8 + 2 = 42. Moving a digit one position left multiplies its value by two.
2 in Binary
× 2× 1
10: one two and zero ones.
42 in Binary
× 32× 16× 8× 4× 2× 1
101010: 32 + 8 + 2 = 42.
181 in Binary
× 128× 64× 32× 16× 8× 4× 2× 1
NASA’s example: 10110101 = 128 + 32 + 16 + 4 + 1.
255 in Binary
× 128× 64× 32× 16× 8× 4× 2× 1
11111111: eight 1 bits add up to 255.
Enter a nonnegative whole number in decimal. Output uses at most 256 binary digits and omits the optional 0b prefix and leading zeros. Signed, fractional, and fixed-width machine encodings are outside this converter.
History
Leibniz described arithmetic with only 0 and 1 in a 1703 account. Binary place value later became central to digital computing, where each bit has two possible values. This entry presents the modern computing notation rather than assigning binary a single place or date of invention.
How to read it
Read from left to right, using only 0 and 1. From the right, the places are worth 1, 2, 4, 8, 16, 32, and so on. Add the places that contain a 1.
- There are two digits: 0 and 1. Each position to the left is worth twice as much as the previous one.
- For 101010, label the places from left to right: 32, 16, 8, 4, 2, 1.
- The 1 digits contribute 32, 8, and 2. The 0 digits keep the other positions empty.
- Add 32 + 8 + 2 = 42. Moving a digit one position left multiplies its value by two.
Limits
Enter a nonnegative whole number in decimal. Output uses at most 256 binary digits and omits the optional 0b prefix and leading zeros. Signed, fractional, and fixed-width machine encodings are outside this converter.
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