8–10 Marks • 100% Accuracy
Digital Circuits — Complete Revision Notes
1. Boolean Algebra & Logic Minimization
Essential Laws & K-Map Grouping
- Absorption Law: $A + AB = A$, $A(A + B) = A$.
- Redundance (Elimination) Law: $A + \bar{A}B = A + B$, $\bar{A} + AB = \bar{A} + B$.
- Consensus Theorem: $AB + \bar{A}C + BC = AB + \bar{A}C$ (The redundant term is $BC$). Dual: $(A+B)(\bar{A}+C)(B+C) = (A+B)(\bar{A}+C)$.
- Universal Gates: NAND and NOR can realize any Boolean function. Minimum NANDs for: NOT (1), AND (2), OR (3), NOR (4), XOR (4), XNOR (5).
2. Combinational Circuit Design
Multiplexers, Decoders & Adders
- Multiplexer (MUX) as Universal Block: A $2^n \times 1$ MUX can implement any function of $n$ variables directly without external gates, or $(n+1)$ variables with inversion.
- Decoder with Enable: Active-low $n$-to-$2^n$ decoder outputs minterms directly. By connecting NAND gates to decoder outputs, any SOP expression can be synthesized.
- Half & Full Adders: Full Adder: $\text{Sum} = A \oplus B \oplus C_{in}$, $\text{Carry} = AB + BC_{in} + AC_{in}$. A Full Adder can be built from 2 Half Adders and 1 OR gate (or 9 NAND gates).
3. Sequential Circuits & Counters
Flip-Flop Characteristic Equations & Modulus
| Flip-Flop | Next State Equation $Q_{n+1}$ | Excitation Condition ($0\to 1$) | Excitation Condition ($1\to 0$) |
|---|---|---|---|
| S-R | $S + \bar{R}Q_n$ ($SR=0$) | $S=1, R=0$ | $S=0, R=1$ |
| J-K | $J\bar{Q}_n + \bar{K}Q_n$ | $J=1, K=X$ | $J=X, K=1$ |
| D | $D$ | $D=1$ | $D=0$ |
| T | $T \oplus Q_n$ | $T=1$ | $T=1$ |
Other GATE ECE Revision Notes
Engineering Mathematics →
Linear Algebra, Calculus, Euler-Cauchy ODEs, Complex Variables, Probability & Statistics
Signals & Systems →
LTI Convolution, CTFT, DTFT, Laplace ROC, Z-Transform, Nyquist Sampling
Network Theory →
Thevenin, Norton, Max Power, Transient Step Response, AC Resonance, Two-Port Matrices
Communication Systems →
AM, FM, Carson's Rule, PCM Quantization SNR, BPSK, QPSK, Shannon Channel Capacity
Analog Circuits →
Diodes, Small-Signal BJT & MOSFET, Op-Amp Virtual Ground, Active Filters, Oscillators
Control Systems →
Mason's Gain, 2nd Order Transient Specs, Routh-Hurwitz, Root Locus, Bode & Nyquist
Electromagnetics →
Maxwell's Equations, Plane Wave Reflection, Transmission Lines, Smith Chart, Waveguides
General Aptitude →
Numerical Reasoning, Spatial Reasoning, Speed-Distance, Permutations, Probability