数字电路ch3waveformsandbooleanalgebra.ppt

《数字电子学》电子教案 理学院物理系：张雷 EXAMPLE 3-39 EXAMPLE 3-40 Notice that the A input did not appear in the final circuit. It was not needed to produce the required output. EXAMPLE 3-41 Theorem 4. A · 1=A EXAMPLE 3-17 Theorem 5. A+1=1 EXAMPLE 3-18 Theorem 6. EXAMPLE 3-19 Theorem 7. EXAMPLE 3-20 Theorem 8. EXAMPLE 3-21 EXAMPLE 3-22 EXAMPLE 3-23 Theorem 9. EXAMPLE 3-24 Theorem 10. EXAMPLE 3-25 EXAMPLE 3-26 EXAMPLE 3-27 Theorem 11. EXAMPLE 3-28 EXAMPLE 3-29 EXAMPLE 3-30 3.5 DEMORGANS THEOREMS Theorem 1. This theorem reinforces the fact that a NAND is the same as inverting the inputs into an OR. Theorem 2. This theorem supports the fact that a NOR is the same as inverting the inputs into an AND. To apply DeMorgans theorems successfully, you must be able to identify the terms of an expression. AB + CDE + FG ——AB, CDE, and FG are ORed together. (A + B) (C + D) —— A + B and C + D are ANDed together. (A + B) (C + D) + EFC ——(A + B) (C + D) and EFG are ORed together. ABC ——A, B, and C are ANDed together. To implement DeMorgans theorems, follow these three steps: Step 1. Complement the entire expression. Step 2. Change the function between each term. Step 3. Complement each term. EXAMPLE 3-31 EXAMPLE 3-32 EXAMPLE 3-33 EXAMPLE 3-34 Figures 3-34A and B show the original and modified circuits. To confirm that these two circuits are equivalent, develop a truth table for each circuit. The two truth tables should be identical. EXAMPLE 3-35 To confirm that these two circuits are equivalent, develop a truth table for each circuit. The two truth tables should be identical. The truth tables are identical: the circuits are equivalent. 3.6 DESIGNING LOGIC CIRCUITS Method 1——Boolean Algebra EXAMPLE 3-36 EXAMPLE 3-37 This is identical to the original truth table. EXAMPLE 3-38 * Chapter 3: Waveforms and Boolean Algebra DIGITAL SYSTEM APPLICATION OBJECTIVES Combine signals from a shift counter and predict the outputs. Select shift counter signals and gates