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# Minimization Definition/Meaning:

1. The process of manipulating a logical expression and thereby transforming it into a simpler but equivalent expression with the same truth table. In practice this commonly means reducing the number of logic gates, number of gate inputs, or number of logic levels in a combinational circuit that realizes the logical expression. Minimization methods include use of Karnaugh maps and algebraic manipulation (often computer-aided).

2. A process whereby a new function can be obtained from an old function using the minimization or μ-operator, which is defined as follows. Let g be a function of n+ 1 variables taking nonnegative integer values and having the integers as its range. Then

μy(g(x1,x2,.....,xn,y) = 0)

produces the least nonnegative integer y for which

g(x1,x2,.....,xn,y) = 0

for the fixed x1,x2,.....,xn. Of course, such a y may not exist. If y does exist a new partial function ƒ of n variables can be defined from g by applying the μ operator:

ƒ(x1,.....,xn) = μy(g(x1,.....,xn,y) = 0)

Otherwise ƒ(x1,.....,xn) is undefined. To illustrate the use of minimization, let ƒ be defined as follows:

ƒ(x) = μy(| 2y - x| = 0)

Then ƒ = x/2 when x is even.

## Near by Terms:

 MICR Micro Microcircuit Microcode Microcomputer Microcontroller Microdata Microinstruction Microprocessor Microprogramming Microprogram Sequencer Microprogram Store (control memory) Microsequence Middleware MIMD Processor Min Minicomputer (mini) Minimal Machine Minimax Procedure Minimization Minimum-Access Code Minterm (standard product term) Mixed Logic Mixed-Radix System

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