EXAMEN 2

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 ​

SOP= A’BC’D’​

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