# EXAMEN 2

Classified in Computers

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**j-cube**is 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 **implicant**is
A cube of any order (1-,2-,or 3-cube)

A **j-cube**is
Called a **prime
Implicant** if it cannot be combined with another**j-cube**
To form a **(j+1)-cube**.

If a 1-cell can exist in one and only one **prime** **implicant**, it
Is called a**distinguished 1-cell**.

A **prime implicant**is called an **essential prime implicant**if 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