Why base-2 is simpler than you think — and why every computer depends on it
Our everyday number system is base-10 (decimal) because it uses ten digits: 0 through 9. The binary number system is base-2 because it uses only two digits: 0 and 1. The "base" tells you how many unique digits the system uses before it needs to add a new position.
In decimal, when you pass 9, you add a new position: 10. In binary, when you pass 1, you add a new position: 10 (which is "two" in decimal). This is the only confusing part — "10" in binary does not mean ten. It means two. The same symbols, different meaning depending on the base.
Every digit position in binary represents a power of 2, starting from the rightmost digit:
| Position (from right) | 7th | 6th | 5th | 4th | 3rd | 2nd | 1st |
|---|---|---|---|---|---|---|---|
| Power of 2 | 2⁶ = 64 | 2⁵ = 32 | 2⁴ = 16 | 2³ = 8 | 2² = 4 | 2¹ = 2 | 2⁰ = 1 |
To convert binary to decimal: multiply each bit by its position value and add them up. 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 8 + 0 + 2 + 1 = 11.
With 8 bits, you can count from 0 (00000000) to 255 (11111111). This is why 8-bit computers worked with values from 0-255, why RGB colors go from 0-255, and why the byte became the fundamental unit of digital storage.
Decimal 0 = Binary 0000
Decimal 1 = Binary 0001
Decimal 2 = Binary 0010
Decimal 3 = Binary 0011
Decimal 4 = Binary 0100
Decimal 5 = Binary 0101
Decimal 6 = Binary 0110
Decimal 7 = Binary 0111
Decimal 8 = Binary 1000
Decimal 9 = Binary 1001
Decimal 10 = Binary 1010
Decimal 11 = Binary 1011
Decimal 12 = Binary 1100
Decimal 13 = Binary 1101
Decimal 14 = Binary 1110
Decimal 15 = Binary 1111
Notice the pattern: the rightmost bit alternates 0,1,0,1. The second-from-right alternates 0,0,1,1,0,0,1,1. Each position toggles at half the frequency of the one to its right. This elegant pattern is why binary circuits are so simple to build — each bit is just a flip-flop toggling at a predictable rate.
Practice with our free binary to decimal converter to test your understanding.