Chapter 2 Gates
2019/2/27 Binary Logic Deals with binary variables that take 2 discrete values (0 and 1), and with logic operations Three basic logic operations: AND, OR, NOT Binary/logic variables are typically represented as letters: A,B,C,…,X,Y,Z Boolean Algebra 2019/2/27 Boolean Algebra
NOT Gate -- Inverter X Y 1 1
AND Gate AND X Y Z 0 0 0 0 1 0 1 0 0 1 1 1 X Z Y Z = X & Y
OR Gate OR X Y Z 0 0 0 0 1 1 1 0 1 1 1 1 X Z Y Z = X | Y
Basic Logic Gates and Basic Digital Design NOT, AND, and OR Gates NAND and NOR Gates DeMorgan’s Theorem Exclusive-OR (XOR) Gate Multiple-input Gates
NAND Gate NAND X Y Z 0 0 1 0 1 1 1 0 1 1 1 0 X Z Y
NAND Gate NOT-AND X Y W Z 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 X W Z Y
NOR Gate NOR X Y Z 0 0 1 0 1 0 1 0 0 1 1 0 X Z Y
NOR Gate NOT-OR X Y W Z 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 X W Z Y
NAND Gate X X Z Z = Y Y X Y W Z 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 X Y ~X ~Y Z 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0
NOR Gate X X Z Z Y Y X Y Z X Y ~X ~Y Z 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 X Y ~X ~Y Z 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0
Exclusive-OR Gate XOR X Y Z X Z 0 0 0 Y 0 1 1 1 0 1 1 1 0
Exclusive-NOR Gate XNOR X Y Z X Z 0 0 1 Y 0 1 0 1 0 0 1 1 1
Multiple-input AND Gate Z 1 Output is HIGH only if all inputs are HIGH Z 1 An open input will float HIGH
Multiple-input OR Gate Z 2 Output is LOW only if all inputs are LOW Z 2
Multiple-input NAND Gate Z 3 Output is LOW only if all inputs are HIGH Z 3
Multiple-input NOR Gate Z 4 Output is HIGH only if all inputs are LOW Z 4
Universal Gates Proving NAND gate is universal
NOR Gate (Universal) Proving NOR gate is universal
Logic Chips (cont.) Integration levels SSI (small scale integration) Introduced in late 1960s 1-10 gates (previous examples) MSI (medium scale integration) 10-100 gates LSI (large scale integration) Introduced in early 1970s 100-10,000 gates VLSI (very large scale integration) Introduced in late 1970s More than 10,000 gates
Logic Design 3-input majority function A B C F 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Logical expression form F = A B + B C + A C