Digital Logic

Explore basic concepts in digital logic by covering numerical representation, the system, the representation of numbers, and binary quantities.

Explore numerical representation by contrasting analog and digital quantities, with examples like speedometers, thermometers, microphones, tape recorders, digital clocks, and marble counting.

Explore how analog, digital, and hybrid systems process inputs into outputs, and how analog–digital and digital–analog conversions enable temperature control and audio recording.

Explore decimal, binary, octal, and hexadecimal number representations, focusing on the decimal base ten, its ten numerals 0–9, and the positional weights illustrated by examples.

Learn how the binary system represents numbers with base two using digits 0 and 1. Practice binary counting and identify most and least significant digits.

Convert decimal numbers to binary by dividing by two, collecting remainders, and assembling bits from right to left. For example, 45 becomes 101101 and 11.625 becomes 1011.101.

Learn to convert binary numbers to decimal by weighting each digit with powers of two and summing the results for both whole and fractional parts.

Explore binary quantities and how digital systems represent information with two states, using examples like switches, diodes, transistors, and timing diagrams, and discuss positive and negative logic in integrated circuits.

Compare parallel transmission, using many wires to send data at once, with serial transmission, which uses a single line and transmits bits one by one. Examine memory concepts, distinguishing known memory from memory, and map data flow within a digital computer’s input, control unit, arithmetic and logic unit, memory unit, and output.

Explore octal and hexadecimal representations and their conversions, plus other number conversions, complement representations, binary numbers and arithmetic, binary codes including bcd code, alphanumeric codes, and essential terms and definitions.

convert decimal to octal using two methods: repeated division by eight with remainders, and first converting to binary then to octal; includes handling fractional parts by multiplication by eight.

Convert octal numbers to decimal by multiplying each digit by eight raised to its position and summing the results, as shown for 1061 octal equals 561 decimal.

Understand hexadecimal representation, using 0–9 and A–F, with examples, hex sequence rules, and weightages based on powers of 16.

Learn two methods to convert decimal to hexadecimal: division by 16 with remainders, or binary-to-hex regrouping. See fractional conversion illustrated by 78.55 becoming 4.8c hex via repeated multiplication by 16.

Convert hexadecimal to decimal by applying weightages to each digit with powers of 16 and summing the results, as shown: 167 hex equals 359 decimal.

Convert binary to hexadecimal by grouping four bits from right to left and translating each nibble to hex digits, and apply to fractional binaries with zeros padding around decimal point.

Translate octal to binary by converting each octal digit to its three-bit equivalent and preserving the original digit order and the decimal point, as shown with 137_8 and 52.3_8.

Convert hexadecimal to binary by turning each digit into a four-bit block and preserving its position. The lecture uses a7 and e9.1 to illustrate left-to-right placement and a decimal point.

Convert decimal numbers to base k using division and remainders, and convert from base k to decimal by weighting digits. Use direct and two-step methods for decimal, binary, octal, hexadecimal.

Explain the definition of complements and derive one's and two's complement, including shortcut methods, with binary, decimal, octal, and hexadecimal examples for subtracting and storing negative numbers.

Explore how signed binary numbers are stored in memory across eight, sixteen, or more bits, using sign bits and conventions like unsigned, two's complement, one's complement, and sign magnitude.

Explore binary arithmetic in digital logic, including addition and subtraction using complements. Learn how same-sign and different-sign cases influence calculations for both operations.

Explore binary arithmetic addition for same-sign numbers in eight-bit words. Add positive values like 13 and 4 to get 17, then add negatives using two's complement to obtain -17.

Demonstrates adding numbers with different signs in an eight-bit system, converting negatives to two's complement, discarding the extra bit, and determining the final sign by the larger magnitude.

Subtract binary numbers with the same sign in eight-bit memory by converting to two's complement and adding; plus 13 minus plus 4 yields 9, and -13 minus -4 yields -9.

Explore subtraction of different-sign numbers in eight-bit arithmetic using two's complement, illustrated by case 1 with +13 and -4 and case 2 with -13 and +4, yielding 17 and -17.

Explore how binary codes represent decimal digits, alphabets, and symbols using n-bit combinations, and compare weighted vs non-weighted and self-complementing vs non-self-complementing codes with examples.

Explain how bcd code uses four weighted bits (8-4-2-1) to represent decimal digits, enables decimal to bcd conversion, and guides bcd addition with six corrections for invalid results.

Explore gray code, a non-weighted binary sequence where only one bit changes between successive numbers, and learn its binary-to-gray and gray-to-binary conversions, plus error-avoidance advantages.

The 2421 code is a four-bit weighted code for digits 0–9, with weights 2, 4, 2, 1, where 1101 encodes 7 and its 0010 complement equals 2, illustrating self-complementing behavior.

Explore excess-3 code, a binary encoding that adds three to each decimal digit, uses four-bit non-weighted representations, and is self-complementing through its ones' complement relation.

Explore the eight four minus two minus one code, a 4-bit weighted code for decimal digits, and learn how to convert between decimal digits and this self-complementing code.

Explore alphanumeric codes like ASCII, EBCDIC, and Unicode, noting seven-bit ASCII for 128 characters with 94 printable and 34 control characters, and compare EBCDIC to Unicode encoding.

Explore the fundamentals of digital logic, including bits, bytes, nibble, words, and registers, and learn how parity methods including even and odd parity enable basic error detection.

Explore boolean gates and theorems in digital logic, covering binary constants and variables, truth tables, or and gates, nor and nand gates, boolean algebra rules, and minterms and maxterms.

Learn the basics of Boolean constants and variables, logic gates, Boolean algebra, and Boolean functions, and use truth tables to relate inputs to outputs.

Explore the or operation in boolean algebra and how an or gate outputs one when any input is one. See the truth table, symbol, and multi-input cases.

Explore the and operation in Boolean algebra using the and gate, where x equals a and b only when both inputs are true, as shown by the truth table.

Explore the not operation in digital logic, showing how the not gate inverts a single input to its complement, with truth table, inverter symbol, and waveform examples.

Explore the rules of Boolean algebra, emphasizing parentheses priority and gate precedence for and, or, and not. Solve gate logic circuits step by step with case-based examples.

Explore four methods to solve boolean expressions: case one simplifies by substituting values; case two uses circuit diagrams. Case three employs truth tables; case four forms circuits from expressions.

Explain nor and nand gates as or and and gates followed by an inverter, detailing their symbols, two-input truth tables, and boolean expressions.

Explore core boolean theorems for and and or operations, including x·0=0, x·1=x, x·x=x, x·x̄=0, x+0=x, x+1=1, x+x=x, x+x̄=1, and reinforce commutative, associative, and distributive laws.

Explains the involution law from theorem 14, where double negation yields the original term, and presents absorption laws (theorem 15a, 15b) and duals (theorem 16a, 16b) for simplification.

This lecture presents De Morgan's theorems in boolean logic, proving (x + y)' = x' y' and (xy)' = x' + y', with p and p' and related theorems.

Explore the universality of nand gates, showing how any boolean function or basic gate can be implemented using nand forms, via two-level and multi-level circuit conversion with bubbles.

Explore the universality of nor gates by converting or gates and and gates into nor configurations, using two-level and multi-level implementations, with bubble techniques to realize complex circuits.

Explore minterms and maxterms as the canonical forms of boolean functions, using truth tables to derive sum-of-products and product-of-sums representations for two- and three-variable cases.

Analyze boolean expressions and truth tables, covering sop and pos forms, the map method, looping pairings, don't-care conditions, xor and xnor gates, parity checkers, and enable/disable circuits.

Explore how digital logics translate among four forms—digital circuits, boolean expressions, truth tables, and simplified boolean expressions—and learn conversion methods using gates, boolean theorems, Cmap, and minterms or maxterms.

Explore the sum of products and product of sums forms in digital logic, including product terms, literals, and inversion rules, with practical examples and conversion steps.

Utilize the map method, or Karnaugh map, to simplify logic equations and convert truth tables into logic circuits using a two-variable four-square representation of minterms.

Learn the three-variable k-map for x, y, z with eight squares and minterms M0–M7, in vertical and horizontal forms, using gray code where adjacent squares differ by one variable.

Explains the four-variable map with a 4x4 grid of 16 minterms in gray code, where adjacent squares differ by one bit, and introduces the five-variable map as two four-variable maps.

Explore looping in k maps to simplify Boolean expressions by grouping ones into loops (octets, quads, pairs). Eliminate complemented variables and derive the final expression.

Explore looping of four pair in digital logic by analyzing seven k-map cases across two to four variables, deriving simplified functions like y, z', and bd.

Explore looping of eight pair in Karnaugh maps, forming octets in four-variable maps and deriving simple expressions such as f = b, f = c̄, or f = d̄.

Apply Karnaugh map techniques to digital logic by forming loops of ones on a four-variable map and deriving simplified boolean functions in sum of product form.

Explore prime implicants in a four-variable map, identify essential prime implicants when a minterm is covered by one, and recall looping relations from four to one literals.

Explore how don't care conditions, marked as x, help form loops in a 3-variable K-map, shown via elevator control with inputs m, f1, f2, f3 and output open.

Explore the xor gate with two inputs, outputting a bar b plus b bar a. See the xnor gate, ab plus a bar b bar, high when inputs match.

An equality detector for two 2-bit numbers using xor/xnor logic, truth table, and k-map; implement with two xnor gates and one nand gate to produce a high output when equal.

Explore parity bits, including even and odd parity, and learn how an XOR-based even parity generator and a receiver-side checker detect errors in transmission.

Explore enable and disable circuits built from basic gates such as and, nand, or, nor to control data flow with permanent control inputs and practical design examples.

Explore the two main types of digital circuits: combinational and sequential, clarifying their definitions, differences, feedback, memory, timing, and typical building blocks like logic gates and flip-flops.

Define and classify combination circuits, then cover topics from half and full adders and subtractors to multiplexers, decoders, encoders, PLD, and seven-segment converters.

Define combinational circuits and classify them into arithmetic logical functions, data transmission, and code converters, noting outputs depend on the present state of the input and the absence of memory.

Explore how a half adder adds two one-bit digits to produce sum and carry, using minterm expressions and an XOR-based circuit.

Compute the difference and borrow with a two-input half subtractor, where the difference equals x xor y and the borrow equals not x and y.

Learn how a full adder adds three one-bit inputs to produce sum and carry. Examine its truth table and k maps, derive minterms, and review block diagrams and two-half-adder implementations.

Analyze the full subtractor as a three-input, two-output combinational circuit, and build its truth table, k-map, and block diagram, noting the difference and borrow outputs.

Explore how a binary adder uses cascaded full adders to sum two binary numbers, propagate carries, and employ a carry lookahead generator to meet carry propagation, illustrated with four-bit example.

Convert subtraction to addition by using two's complement of b (one's complement plus one) and adding to a with not gates and full adders, noting overflow.

Four-bit binary adder-subtractor circuit adds or subtracts numbers using an external m input, inverting b with xor gates when m=1 across the full adders.

Explore how a four-bit BCD adder, a combinational circuit, adds two BCD numbers using two four-bit binary adders, with logic to add six when the sum exceeds nine.

Explore how binary multiplier uses combinational circuits to multiply binary numbers through partial products, left shifts, and summation with and gates, half adders, and full adders.

Explore digital comparators, including equality and magnitude ones, as binary logic circuits that compare two n-bit numbers to output less than, equal, or greater than signals.

Explore how a multiplexer selects binary data from multiple inputs to a single output using selection lines, enable control, and examples like 2-to-1 and 4-to-1 configurations.

Explains the demultiplexer, a data transmission circuit that routes one input to multiple outputs using selection lines and an enable input; covers 1 to 2 and 1 to 4 types.