We use the axioms and theorems of Boolean algebra to optimize our designs. Design goals vary. " Reduce the number of inputs? " Reduce the number of gates? " Reduce number of gate …

• Used to build logic functions • There are seven basic logic gates: AND, OR, NOT, NAND (not AND), NOR (not OR), XOR, and XNOR (not XOR) [later]

Maurice Karnaugh developed the Karnaugh Map at Bell Labs in 1953 K-maps come from venn diagrams Previously in recitation, we looked at simplifying boolean expressions using …

Any logic function can be implemented using only NANDs (or, equivalently, NORs). Note that chaining/treeing technique doesn’t work directly for creating wide fan-in NAND or NOR gates.

Combinational logic gates evaluate Boolean expressions. They can do computation, decoding (e.g. mapping of one binary number to another binary number), selection (such as multiplexers …

Pushing bubbles backward (from the output) or forward (from the inputs) changes the body of the gate from AND to OR or vice versa. Pushing a bubble from the output back to the inputs puts …

1. Simplify the following Boolean expression using Karnaugh Map: A′B+AB′+A′B′CA'B + AB' + A'B'CA′B+AB′+A′B′C. Explain the steps in detail. 2. Describe the Tabulation Method for …

Logic gates may be combined to form logic gate diagrams that perform more complicated logical operations. Truth tables are used to show the states of each terminal and hence the logical …

More than one Logic Circuit can implement same Logic function. Use Algebra (Identities) or Truth Tables to show equivalence. Any logic function can be implemented as “sum of products”. …

Boolean Expression to Logic Circuit : Use AND gates for the AND operators, OR gates for the OR operators, and inverters for the NOT operator. Wire up the gates the match the structure of the …

Logic gates are the switches that turn ON or OFF depending on what the user is doing! They are the building blocks for how computers work. What are logic gates? Let’s do an example! …

The more widely used maps are the three and four variable maps, which are shown in Figure 2 and Figure 3 respectively. Figure 2: A three variable Karnaugh map. Figure 3: A four variable …

More than one Logic Circuit can implement same Logic function. Use Algebra (Identities) or Truth Tables to show equivalence. Any logic function can be implemented as “sum of products”. …

Examples show constructing truth tables and mapping them to minimize logic expressions using K-maps.

Logic Gates Use switch behavior of MOS transistors to implement logical functions: AND, OR, NOT.

Questions for think, pair, share: What do Karnaugh maps do for us? What special rules do we need to follow to use Karnaugh maps? Try to use a Karnaugh Map to simplify the formula from …

Task 1: Exploring Basic Logic Gates Place the AND gate chip on the breadboard. Use the 2230 power supply to supply power to the chip. Connect the first input (bo) to the 0 bit on the PG …