Phase 1 Master Exam Bank: Foundations, Signals & Channel Capacity

Data Communications is the exchange of data between two devices via a transmission medium governed by protocol rules.

A Computer Network is an interconnected collection of autonomous computing devices capable of routing traffic, sharing hardware resources, and delivering services.

Data Communications provides theoretical rules, signals, and protocol mechanics; Computer Networks is the practical hardware deployment and real-world implementation.

1. Message (Data payload) 2. Sender (Origin unit) 3. Receiver (Destination unit) 4. Medium (Guided/Unguided path) 5. Protocol (Governing rules)

The actual data information being sent (text, audio, video, picture).

The originating device hardware capable of transmitting a signal across a medium.

The target device hardware designated to receive and process a signal.

The physical path traversed by a signal from sender to receiver.

A set of governing rules synchronizing communication formatting, timing, and sequence.

Without a protocol, devices can physically send signals but cannot parse or interpret the bit stream.

Unidirectional communication (e.g. FM Radio, Television broadcast, Keyboard to PC).

Bidirectional communication, one direction at a time (e.g. Walkie-Talkies, Legacy Hubs).

Simultaneous bidirectional communication (e.g. Modern Switches, Telephone call).

Physical solid conductors (CAT6 UTP, STP, Coaxial, Fiber Optic).

Wireless electromagnetic transmission through air/vacuum (Wi-Fi RF, Microwave, Infrared).

Water short-circuits copper conductors and strongly absorbs/scatters 2.4GHz/5GHz radio waves.

1. File & resource sharing 2. Peripheral sharing 3. Centralized administration 4. Cost reduction

Continuous electromagnetic waveform changing smoothly over time.

Discrete sequence of voltage levels representing binary 1s and 0s.

Maximum absolute voltage or signal strength value attained by a signal.

Number of complete cycles per second, measured in Hertz (Hz).

Time required to complete one full cycle (T = 1 / f).

Position of a wave relative to time t = 0 in degrees or radians.

Number of bits sent per second (bps).

Number of signal symbol state changes per second.

When each symbol carries exactly 1 bit (M = 2).

Loss of signal strength/amplitude as a signal propagates through a medium.

Decibels (dB = 10 * log10(P_out / P_in)).

Composite signal alteration caused by different frequency components traveling at varying speeds.

Random electron agitation in conductors creating background noise.

Bit Rate = 2 * B * log2(M) = 2 * 4000 * log2(2) = 8,000 bps (8 Kbps).

Bit Rate = 2 * B * log2(M) = 2 * 4000 * log2(16) = 32,000 bps (32 Kbps).

C = B * log2(1 + SNR) = 1,000,000 * log2(64) = 6,000,000 bps (6 Mbps).

20 = 10 * log10(SNR) => log10(SNR) = 2 => SNR = 10^2 = 100.

T_p = distance / speed = 2,000,000 / 2*10^8 = 0.01s = 10 ms.

Bits = 12,000. T_t = 12,000 / 100,000,000 = 0.12 ms.

dB = 10 * log10(10 / 100) = 10 * log10(0.1) = -10 dB (10 dB loss).

Bits per symbol = log2(8) = 3. Baud Rate = 7200 / 3 = 2400 Baud.

Guarantees a voltage transition in the middle of every bit period for clock synchronization.

Baseband sends digital signals directly without modulation. Broadband modulates digital data onto high-frequency carrier waves.

1. Shannon Capacity C = 1,000,000 * log2(1+31) = 5 Mbps. 2. Nyquist: 5,000,000 = 2 * 1,000,000 * log2(M) => M = 2^2.5 = 5.65 => Must use M = 6 signal levels.

Round-trip time 2*T_p across 2,500m cable = 51.2 microseconds slot time. At 10 Mbps, min bits = 10^7 * 51.2*10^-6 = 512 bits = 64 bytes.

T_t = 1ms, T_p = 5ms. Efficiency = T_t / (T_t + 2*T_p) = 1 / (1 + 10) = 9.09%.

SNR = 10^(30/10) = 1000. C = 3100 * log2(1001) = 30.9 Kbps.

Total latency for 3 packets across 4 hops = (Hops + Packets - 1) * T_t = (4 + 3 - 1) * 1ms = 6 ms.

PCM samples amplitude at Nyquist rate (8kHz) and quantizes to 8-bit PCM (64Kbps). Delta modulation encodes only the +1/-1 change.

Maps 4-bit nibbles into 5-bit symbols to eliminate long runs of zeros, ensuring clock synchronization before NRZ-I line encoding.

T_b = 1 / (40 * 10^9) = 25 picoseconds.

As B -> infinity, C = (S / N0) * log2(e) = 1.44 * S / N0.

Uses 5 voltage levels across 4 wire pairs transmitting 2 bits per symbol per pair at 125 Mbaud (125 * 2 * 4 = 1000 Mbps).

Academic derivation for signal capacity problem 11 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 12 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 13 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 14 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 15 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 16 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 17 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 18 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 19 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 20 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 21 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 22 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 23 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 24 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 25 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 26 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 27 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 28 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 29 analyzing decibel budget, thermal noise spectral density, and transmission limits.

Academic derivation for signal capacity problem 30 analyzing decibel budget, thermal noise spectral density, and transmission limits.