Binary Data Representation

Binary representation is fundamental to digital systems. Each piece of data is represented as a sequence of bits (binary digits), where each bit can be either 1 or 0. This demonstration shows how a decimal number is converted to binary and transmitted as a digital signal, including error detection mechanisms.

Transmission Speed and Baud Rate

The speed at which digital signals are transmitted is measured in baud rate - the number of signal changes possible per second. In this simple example, we're using binary signals where 1 baud = 1 bit per second (bps). With each bit taking 1μs, this represents a 1 Mbaud (1 million baud) signaling rate. More complex encoding schemes can pack multiple bits per signal change, making the actual data rate higher than the baud rate.

0b71b61b51b41b30b21b11b00PThreshold0μs1μs2μs3μs4μs5μs6μs7μs8μs

Signal Properties

  • Each bit occupies one clock cycle (1μs) - equivalent to 1 Mbaud signaling rate
  • High frequency noise stays within threshold bounds - signal remains intact
  • Low frequency noise can corrupt bit 4 - parity check will detect this error
  • Dual bit errors (bits 2 and 6) fool parity check as total number of 1s remains even

Modbus RTU Transmission Time Comparison

0ms100ms200ms300ms400ms500ms600ms700ms800ms900ms1000ms9600 baud238.3ms115200 baud19.9msHeaderData (200 bytes)CRC

Packet composition: 8 header bytes + 200 data bytes (100 registers) + CRC

Each byte requires 11 bits (8 data + 1 start + 1 stop + 1 parity)

Total bits transmitted: 208 bytes × 11 bits = 2288 bits

Error Detection and Noise Immunity

Digital systems use various error detection methods to ensure data integrity. The simple parity bit shown above is just one example - it makes the total number of 1s even, allowing detection of single-bit errors. More sophisticated methods like CRC (Cyclic Redundancy Check) provide even better error detection capabilities.

The threshold-based nature of digital signals provides excellent noise immunity. As long as noise doesn't push the signal past the threshold, the original data can be recovered perfectly. This is one of the key advantages of digital over analog transmission.