Binary Place Value Counter

Click any bit switch or use the controls below to discover how positional base-2 notation forms numbers.

Decimal (Base 10)

Binary (Base 2)

00000000

Hexadecimal (Base 16)

0x00

Active Bits (Sum)

0 of 8 bits

How Binary Place Values Work

In standard decimal (Base-10), each place value is a power of 10 ($10^0=1, 10^1=10, 10^2=100$). Binary (Base-2) works identically, but place values double with each step to the left ($2^0=1, 2^1=2, 2^2=4$, etc.).

Bit State: 0 vs 1 A bit is an on/off switch. When '1', add its place weight to the total sum.

Byte Capacity An 8-bit byte can represent $2^8 = 256$ distinct combinations (0 through 255).

Powers of 2 $128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255$. All bits ON equals the maximum value.

Why one bit changes a number by its place weight

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Read the explanation

The counter has eight bit weights: one, two, four, eight, sixteen, thirty two, sixty four, and one hundred twenty eight, increasing toward the left. Only enabled weights enter the sum. Its starting value forty two has the thirty two, eight, and two switches enabled, so its binary display is zero zero one zero one zero one zero. Turn on the leftmost switch, worth one hundred twenty eight. The existing forty two remains, so the new total is one hundred seventy. Turn that same switch off and exactly one hundred twenty eight is removed. A bit toggle changes one place weight, not a decimal digit. Invert Bits flips every switch in this eight bit mask. The enabled weights and their complement partition all eight weights, whose sum is two hundred fifty five. Inverting forty two gives two hundred thirteen. Inverting again returns forty two. This is the eight bit complement, not a change to a negative signed number. Eight bits represent two hundred fifty six states, zero through two hundred fifty five. The plus one button uses modulo two hundred fifty six, so two hundred fifty five wraps to zero. Minus one from zero wraps to two hundred fifty five. Direct decimal input behaves differently: values beyond the range are clamped, so entering nine hundred ninety nine displays two hundred fifty five.