A decade counter is a circuit that counts in decimal (from 0 to 9) and is commonly used in digital electronics. It is often implemented using flip-flops and is used for a variety of applications, such as frequency division, time measurement, and sequencing.

Decade counters can be cascaded together to form larger counters with higher counting ranges. When cascading multiple decade counters, the output of one counter is connected to the clock input of the next counter. This allows the counters to count in a sequential manner, with each counter incrementing by 1 when the previous counter reaches its maximum value.

In the case of a three-decade counter, there are three individual decade counters connected in cascade. Each decade counter has four output lines, which can be used to represent the binary-coded decimal (BCD) equivalent of the count value. The BCD representation uses four bits to represent each decimal digit (0 to 9).

Since each decade counter has four output lines, it can represent values from 0 to 9 (2^4 = 16 possible combinations). Therefore, a single decade counter can count from 0 to 9. By cascading three decade counters together, we can extend the counting range from 0 to 999 (3 * 10^2 - 1).

To summarize, a three-decade counter consists of three individual decade counters cascaded together. Each individual decade counter can count from 0 to 9, and by combining them, we can count from 0 to 999. Therefore, a three-decade counter would have three BCD counters.