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Knowing digital logic design is necessary when one designs new CPUs, programs FPGAs, and connects those components to other digital chips.
Sometimes it comes in handy for some kinds of computer programming.
That's why most colleges require a class in "digital logic design" for degrees in computer engineering and electrical engineering.
If you mean Logic as in Electronics, Computers etc... Then Electrical and Electronics Engineers study Logic design including True/False equations, AND/OR/NAND/NOR Gates. Logic design is essential for Electronic/Microprocessor and other electronic equipment design tasks. Entire computers of any complexity can be broken down to individual logic elements.
Boolean Algebra is the study of the algebra of logic whilst Mathematical logic is a way of applying Boolean algebra. Other applications include set theory, digital logic and probability.
Graphic Communication and Graphic Design are not the same major. Graphic design is a program in which you learn design on computers based off of principles of color, 2-D and 3-D design. Graphic communications, however is the study of print and digital media. In graphic communication, it is considered both an art and a science in which you study quality and potentials of printing and digital media.
It allows you to avoid the unnecessary use of excessive logic gates by simplifying.
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The field of micro processors and indeed, processors all build on the knowledge gained from digital circuits. Study it and become rich... so that one day you can design something which is better than the presently used