During the 1670s, Leibniz worked on creating a practical calculator that could multiply, divide, and even extract roots using the binary system. This machine was a significant advancement over Pascal’s rudimentary adding machine and a genuine precursor to the computer. He is typically attributed with the invention of the binary number system, which uses just the digits 0 and 1 in base-2 counting, even though he was aware of earlier concepts dating back to the I Ching of Ancient China. The binary, or base 2, number system, expresses all numbers as a combination of the digits 0 and 1 (rather than the ten digits 0 - 9 used in the normal base 10 system). It is a place value system, but rather than using units, tens, hundreds, thousands, etc (powers of 10), it uses powers of 2: 2, 4, 8, 16, 32, 64, etc.
| Decimal | Binary |
|---|---|
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| e.g. the binary number 110100101 is equivalent to: |
|---|
| 1 × 256 = 256 |
| 1 × 128 = 128 |
| 0 × 64 = 0 |
| 1 × 32 = 32 |
| 0 × 16 = 0 |
| 0 × 8 = 0 |
| 1 × 4 = 4 |
| 0 × 2 = 0 |
| 1 × 1 = 1 |
| all the numbers on L.H.S sums to 411 |
Figure: Binary Number System
In the above figure, the binary number system along with some examples are shown. This ability of binary to be represented by the two phases "on" and "off," later became the foundation of almost all current computer systems, and Leibniz’s documentation was crucial in the development process.