Digital design fundamentals

Explore how binary, octal, and hexadecimal number systems enable efficient digital data representation and conversion, highlighting subscripts for bases and the shift from long binary to concise hex forms.

Learn how to convert a binary number into its decimal equivalent by applying the base-2 conversion rule, with examples like 1001 base 2 equals 9.

Explore how binary bits set the range of representable numbers, from one bit (0–1) to three bits (0–7), showing the rule 0 to 2^n minus 1.

Convert octal numbers to decimal by expanding digits in base eight, using digits 0-7; for example, 57 base eight equals 47 base ten.

Learn how to convert hexadecimal numbers to decimal by expanding digits with powers of 16, using digits 0–9 and letters A–E, and applying a worked example.

Learn to convert decimal numbers to binary using successive division by two, record remainders, and assemble them from bottom to top, with an example converting 38.

Convert decimal numbers to their octal equivalents using division by eight, recording remainders to read the octal result from bottom to top, and verify by octal-to-decimal conversion.

Learn, in digital design fundamentals, how to convert a decimal number to hexadecimal by dividing by sixteen, collecting remainders, and using A–F for 10–15.

Convert binary numbers to octal by padding zeros on the left to three-digit groups, then group triples and map to octal digits, as shown in 64_8 and 132_8.

Learn how to convert binary numbers to hexadecimal equivalents by padding to a multiple of four digits and grouping from right to left into four-digit groups, then translating to hex.

Convert octal to hexadecimal by translating to binary, padding to four-bit groups, and reading hex digits. Convert hexadecimal to octal by converting to binary and regrouping into three-bit groups.

Explore binary arithmetic through binary additions, complements, and subtraction, using carry over, decimal checks, and practical examples.

explains radix complements used to simplify subtraction and logic; shows decimal nine's complement by subtracting from all-9s, and binary one's complement by inverting bits with examples.

Demonstrate binary subtraction with unsigned binary numbers and two complement methods, showing how to compute x minus y, handle positive and negative results, and interpret carries in digital design.

Learn how eight-bit computers use the most significant bit to indicate sign and encode signed numbers with sign magnitude form, ones' complement form, and sign to form.

Explore how binary logic uses zero or one variables, with logical operations realized by logic gates, forming the Boolean algebra that underpins every digital device.

Explore boolean algebra and logic gates, learn how to depict operations with pictorial symbols, equations, and truth tables, using variables A, B, and C.

Explore the not gate, its complement operation that inverts a binary bit (0 to 1, 1 to 0). Learn how the not gate flips input X and its symbol.

Explore the AND gate, a two-input boolean operation where the output is one only when both inputs are one, illustrated with practical park examples.

This lecture explains the or gate, shown as a plus sign, where the output is one if either input is one, and zero only if both inputs are zero.

A buffer gate outputs the same value as its input, performing no operation and serving as a storage element in digital circuits; its output equals its input.

Explore nand and nor gates, showing how the not operation inverts the and operation and how the truth tables are opposite.

Explore exclusive or and exclusive nor gates, with outputs signaling different vs same inputs. Learn the truth table principles and the opposite relation of exclusive not to X.

Explore the properties and axioms of boolean algebra, frame real-world problems into boolean functions, and learn how to evaluate expressions for all binary variable values.

Explore closure, associative, and commutative properties in boolean algebra, along with identity, complement, and distributive rules for and/or operations in boolean expressions.

Explore proofs of postulates in digital design fundamentals, validating the complement postulate and distributive law through truth tables and logic expressions.

Master basic boolean theorems with proofs, including absorption law and Morgan's theorem. Compare truth-table results for X and Y to confirm theorems in digital design fundamentals.

Explore duality in boolean algebra by interchanging operators and identity elements, turning ones into zeros, with examples like X and one = X and X or zero = X.

Explore the complement of a boolean function with multiple variables and apply Morgan's laws to express the complement as the conjunction of the variable complements, A' B' C'.

Explore the algebraic manipulation of boolean functions, learn to simplify and minimize expressions, and apply a map-based method with boolean laws to optimize digital circuits.

Explore canonical and standard forms of boolean expressions by forming minterms and maxterms, deriving the sum of products and product of sums representations from truth tables.

Explore standard and canonical forms II by deriving a truth table for three variables x, y, z, identifying minterms and maxterms, and constructing the s.o.p form from the true outputs.

Learn to simplify a boolean equation in digital design fundamentals by applying distributive law and fundamental boolean algebra laws and properties, working through an example with variables X and Y.

Explore the two-variable Karnaugh map, a grid of squares representing a minimized function, and learn how ones are grouped to form the simplified expression in the two standard forms.

Develop understanding of the three-variable k-map by mapping a truth table into a gray-code (great code) grid, then group ones into 2, 4, or 8 cells to derive F.

Explore a four-variable Karnaugh map for w, x, y, z, filling the grid from bracket values and grouping ones to derive the final function.