Blog #7: The Shapes of Logic

     Logic is the study of valid reasoning. What we discussed today is about Digital Logic and Boolean Algebra.

     Since I am an Applied Mathematics student, studying logic is our foundation. We studied and proved statements, arguments, and truth tables. So this topic is not that new to me. But still, I got excited because this was something familiar. Unlike those previous very mathematical meetings where some of my classmates dread, I was happy to see something familiar in a world unfamiliar to me. Chos.

     In digital logic, we study about computers of course, and how they process information and perform arithmetic. That's where logic gates enter. Logic gates are building blocks of a circuit. They usually have two inputs (see truth tables below, with inputs A and B) and one output, depending on the gate they pass through. Logic 1 means on, high, true, yes, or closed switch. Logic 0 means off, low, false, no, or open switch.

http://www.eetimes.com/document.asp?doc_id=1274508

http://www.schoolphysics.co.uk/age16-19/Electronics/Logic%20gates/text/Logic_gates/index.html

• The NOT gate is just an inverter. The output is just a negation of the input.
• In the AND gate, the output is 1 if both of the inputs are 1. Otherwise, the output is 0. The NAND gate is just its negation.
• In the OR gate, the output is 1 if at least one of the inputs is 1. Otherwise, the output is 0. The NOR gate is just its negation.
• In the XOR gate, the output is 1 if one of the inputs is 1. If the inputs are the same (both 0 or both 1), then the output is 0.

http://gcat.davidson.edu/GcatWiki/index.php/Logic_Gates:_Symbols_and_Truth_Tables

     What I liked about this is that it has shapes, and I know and understand how it is used digitally. Before, in my math subjects, we prove truth tables and the operators (in Boolean Algebra), we memorize identities and theorems. We use them in real life sentences and phrases, or arguments. It is amazing how early people made these statements into logic gates that were made into transistors and used in circuits, and still easy to understand. Before, I do not know why we do all these proving. Now I understand that manufacturers of transistors (composed of logic gates) wanted to cut down the costs of making these gates so they simplified the most complex logic gates.

     Connecting logic gates and analyzing more of its complex forms, and simplifying them is really challenging but it actually is fun! To see what I mean, I recommend you to try experimenting here: http://logic.ly/demo/.

http://heythrop.su/logic-society/