Digital Electronics & Logic Design

Explore the decimal system, base ten, with digits zero through nine. Use the digits times ten raised to their index to express numbers, as in 32 = 3×10^1 + 2×10^0.

learn the binary system, base two, using digits zero and one, counting, carrying over between index positions, and converting binary to decimal with powers of two.

Explore the octal system, base-8 digits (0–7), and how to convert to decimal using the sum of Xi times eight to the power i, 16 octal equals 14 decimal.

Learn how to convert decimal to binary by using powers of two, weighting each bit, subtracting from the decimal value, and obtaining the binary representation.

Convert octal to binary by first translating octal to decimal, then decimal to binary; for example, 132 (base 8) equals 90 (decimal) and 01011010 (binary).

Convert hexadecimal to binary by mapping each hex digit to four binary digits, using AF1 as an example to show the straightforward shortcut and the four-bit representation.

Group binary digits into four-bit sets, add leading zeros when needed, and convert each group to its hexadecimal digit, as in 0010 to 2 and 1111 1010 to FA.

Discover how to represent decimal fractions in binary by splitting into integer and fractional parts, converting the integer (7) to binary, and applying fractional weights like 2^-1, 2^-2, and 2^-3.

Compute ones' complement and two's complement from binary numbers and binary fractions by inverting digits and adding one, with step-by-step examples.

Explore binary arithmetic by adding binary values, carrying bits, and validating results through decimal conversion, exemplified by 1010 plus 0110 equals 10000.

Execute binary subtraction by aligning digits and appending zeros as needed, borrowing as required, and performing per-bit subtraction. Verify results by converting binary to decimal to confirm the final difference.

Perform binary multiplication by forming partial products, shifting for each bit, then adding with carries, and verify by converting the binary result to decimal.

Explore binary subtraction using one's complement, where subtracting B from A becomes A plus the one's complement of B, with carries added to the result.

Subtract binary numbers by converting the subtrahend to its two's complement and adding it to the minuend. Invert bits, add one to the least significant digit, and drop the carry.

Explore digital logic gates and how transistors create binary functions from inputs and outputs. Learn how voltage levels define binary zero and one, and how y equals x transforms signals.

Explore how the inverter gate inverts input X to produce output Y, with Y equal to the inverse of X, and review its truth table.

Explore the two-input and gate with output z, where z equals x times y; examine the truth table to show z is one only when both inputs are one.

Explore how a nor gate uses two inputs, x and y, to produce z, inversion of x or y, with z equal to 1 only when both inputs are zero.

The nand gate uses X and Y and inverts the result to produce Z. It outputs one when either input is zero, and zero when both are one.

The xor gate uses two inputs X and Y to produce output Z, equivalent to a one-bit binary addition, yielding 1 when inputs differ and 0 when equal.

Explore the xnor gate, the inversion of the xor gate, with its circle-output symbol and truth table for inputs x and y that determines the output.

Learn to derive boolean equations from a multi-gate circuit using and, or, xor, and inverter gates, and to simplify them to map to more efficient circuit diagrams.

The commutative law states that the order of terms does not change result; for example, a + b = b + a, and a × b = b × a.

Learn the double negation law in digital logic: invert input A twice with inverters, and the output returns to the original value A.

Explore the idempotent law for digital logic, showing that A or A equals A and A and A equals A, using truth tables for zero and one inputs.

Explore the absorption law in digital logic: (A or B) and A equals A, and observe how swapping the operations still yields A, aiding in simplifying logic equations.

Demonstrate de Morgan's law by showing not(A and B) equals not A or not B, and not(A or B) equals not A and not B, with truth-table validation.

Derive a Boolean algebra expression and translate it into a circuit. Then simplify to A or B or C and compare a six-gate design with a three-input or for optimization.

Explore simplifying a complex boolean expression by applying distributive law, factoring, and the complement and identity laws to reduce it to a single term for digital electronics and logic design.

Apply Morgan's law to expand and simplify a three-variable boolean expression, regrouping with the associated and identity laws to yield A inverted or with C inverted or with B inverted.

Derive the boolean expression from a four-gate circuit with a nand gate, an or gate, and an and gate, then simplify using boolean algebra to a minimal two-input xor expression.

Learn how to convert a boolean expression to a product of sums using max terms that include all inputs, and apply distributive law to obtain the final product of sums.

Extract max terms from the truth table zeros to form a product of sums, using A, B, and C and their literals to build each max term.

Explore Karnaugh maps derived from truth tables to obtain optimized logical expressions and implement minimal circuits, converting A and B inputs into a simplified AND-based expression.

Explore grouping and Karnaugh maps to minimize a boolean expression for a two-variable map, deriving a sum of products form and then a minimized one-gate implementation for the Z output.

Explore a three-input Karnaugh map with inputs A, B, and C, showing how to group four and two ones to derive an optimized boolean expression, including Z = B'.

Explore grouping in a four-input Karnaugh map to derive a minimized boolean expression for z, using group sizes 16, 8, 4, 2, and 1, with overlapping groups.

Learn how to use Karnaugh maps with don't care conditions to maximize groups of ones, derive the simplified boolean expression, and implement an optimized circuit with two gates.

Explore the half adder in digital electronics, deriving sum with an XOR gate and carry with an AND gate from all four input combinations A and B.

Explore the half subtractor with inputs A and B, producing the difference as A xor B and borrow when A is zero and B is one.

Demonstrate building a full adder from two cascaded half adders by deriving the sum as A or B or cin and or-ing the stage carries to produce the carry out.

Explore the carry-lookahead adder, showing how it computes sums and generates carries faster than a parallel adder by using look-ahead carries from previous inputs and the original carry input.

Add four-bit decimal-coded inputs with a binary-coded decimal adder and translate the binary sum into decimal digits via combinatorial logic, as 9 plus 4 equals 13.

the lecture explains priority encoders, where eight inputs map to three outputs and the encoder prioritizes a single active input, producing valid output even when multiple inputs are one.

Demonstrate how a multiplexer routes one of several inputs to a single output using a selection input, with 00 to 11 selecting inputs one to four.

Explore SR flip-flops as sequential circuits that store state using a clock and inputs S and R, producing Q and Q' outputs, including set-reset behavior, truth table, and invalid condition.

Explore the jk flip-flop, which adds extra logic to the sr flip-flop to prevent the invalid j=k=1 condition, toggling the output in the next cycle.

Explains the d flip-flop as a simple sequential circuit that stores the current output and updates it to the next state on the clock edge according to d.

Explore how combinational and sequential circuits work together to store and process information, using logic gates, truth tables, flip-flops, and clocked feedback.

Demonstrate a three-bit counter using three jk flip-flops with combinational logic, showing how j=k=1 toggles on clock edges to count from zero to seven and roll over.