AOI Combinational Design
AOI Logic Analysis: Circuit to Truth Table to Logic Expression
A truth table shows how a logic design’s output respond to ALL combinations of possible inputs
Circuit Simplification: Boolean Algebra
Circuit Simplification: DeMorgan's Theorems
Karnaugh Map
Universal Gates: NAND Logic Design
Process for NAND Implementation:
1.If starting from a logic expression, implement the design with AOI logic. 2.In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NAND equivalent. 3.Redraw the circuit. 4.Identify and eliminate any double inversions (i.e., back-to-back inverters). 5.Redraw the final circuit. |
Universal Gates: NOR Logic Design
Process for NOR Implementation:
1.If starting from a logic expression, implement the design with AOI logic. 2.In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NOR equivalent. 3.Redraw the circuit. 4.Identify and eliminate any double inversions. (i.e. back-to-back inverters) 5.Redraw the final circuit. |
Hexadecimal and Octal Number Systems
Decimal-to-Octal Conversion:
Divide the decimal number by 8; the remainder is the LSB of the octal number Octal-to-Decimal Conversion:
Multiply each bit of the Octal Number by its corresponding bit-weighting factor, then sum up the products |
Seven-Segment Displays
Seven-Segment Displays come in two different configurations; Common Anode and Common Cathode:
–Common Cathode (all LED cathodes are connected)
–Common Anode (all LED anodes are connected)
–Common Cathode (all LED cathodes are connected)
–Common Anode (all LED anodes are connected)
Multiplexers & De-multiplexers
Two's Compliment Arithmetic
The
2’s complement process allows you to easily convert a positive number into its
negative equivalent
Binary Adders: XOR and XNOR
Binary Adder