j-cubeis a grouping of 2jlogically adjacent 1-cells on a K-map for an N- variable function which can be combined to form a product of (n-j) literals. J is a positive integer, 0 £ j £ n.
Therefore for n=4 variables, j=1 cube
21cells à(4-1) literals,
22cells à(4-2) literals, 23cells à(4-3) literals
Note: that a minterm is a 0-cube. A 0-cube is different From a 0-cell. A cell can be made of many cubes
An implicantis A cube of any order (1-,2-,or 3-cube)
A j-cubeis Called a prime Implicant if it cannot be combined with anotherj-cube To form a (j+1)-cube.
If a 1-cell can exist in one and only one prime implicant, it Is called adistinguished 1-cell.
A prime implicantis called an essential prime implicantif it includesat least one distinguished 1-cell.
Prime Implicant can Also be defined as an Implicant ifit is a grouping that cannot be changed
Prime implicant expressions for POS, we do the inverse of what is done in the SOP
For Example: maxterm 5 = 0101
POS = (A + B’ + C + D’)
Single-rail variable or input: Available in Only one form
Double-rail variable or input: Available in Both true and complemented forms. Note: When only single rail signals are used, we Will need an extra gate (inverter) in order to implement double rail
Fan-in limit: A constraint on the number of Inputs to a gate
A circuit is called an n-level circuit if n Is the number of gates in the path with the longest delay. Note: An n-level circuit will affect timing by approximately n gates Delay