Digital Electronics & Logic Design

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.

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.

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

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.

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 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 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.

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.

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.

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 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 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.

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.

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.

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.