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Digital Logic

Digital Logic is a short but scoring GATE CS subject. These lessons cover number representation, Boolean algebra and minimization, and combinational and sequential circuits, with truth tables, K-map groupings and counter sequences generated by small Python programs, so every table and count shown is exact.

Start the first lesson

1Number Representation

  1. Number Systems and CodesPositional number systems, converting between decimal, binary, octal and hexadecimal (integers and fractions), BCD, Gray code and other codes.
  2. Signed Numbers and Binary ArithmeticSign-magnitude, 1's complement and 2's complement, their ranges, addition and subtraction, overflow detection, and sign extension.
  3. Floating-Point Numbers (IEEE 754)Fixed-point versus floating-point, the IEEE 754 single and double formats, biased exponents, normalised and denormalised numbers, special values, conversions in both directions, and precision.

2Boolean Algebra and Gates

  1. Boolean AlgebraBoolean operations and laws, De Morgan's theorems, duality, canonical sum-of-products and product-of-sums forms, minterms and maxterms, and counting Boolean functions.
  2. Logic Gates and Universal GatesThe basic gates and their truth tables, XOR and XNOR properties, NAND and NOR as universal gates, gate counts for common functions, and analysing gate circuits.
  3. K-Maps and MinimizationKarnaugh maps for 2 to 4 variables, grouping rules, prime and essential prime implicants, don't-care conditions, minimal SOP and POS, and the Quine–McCluskey method.

3Combinational and Sequential Circuits

  1. Combinational CircuitsHalf and full adders, ripple-carry and carry-lookahead adders with their delays, subtractors, multiplexers and implementing functions with them, decoders, encoders and comparators.
  2. Latches and Flip-FlopsSequential circuits and memory, the SR latch, level- and edge-triggering, SR, D, JK and T flip-flops with characteristic and excitation tables, race-around, converting between flip-flops, and timing limits.
  3. Counters and Shift RegistersRipple (asynchronous) and synchronous counters, mod-N counters, designing a counter from its state sequence, ring and Johnson counters, shift registers, and analysing a sequential circuit by tracing its states.

4GATE Practice

  1. Digital Logic GATE Practice SetMixed GATE-style questions on number systems, 2's complement, IEEE 754, Boolean functions, K-map minimization, combinational circuits, flip-flops and counters.