逻辑与计算机设计基础 复习课件 浙江大学

Chapter 2
▪ Other gates
• Buffer, NAND, NOR, 3-state buffer (Hi-Z), XOR, XNOR
▪ Exclusive-OR operator and gates
• Identities of XOR operation:
▪ X⊕Y’ = X’⊕Y =(X⊕Y)’ X⊕(Y⊕Z)’ = (X⊕Y)’⊕Z = (X⊕Y ⊕Z)’
XNOR gate. Podd=X⊕Y⊕Z, Peven= Podd’=(X⊕Y⊕Z)’
▪ High-impedance outputs
• 3-state buffer (Hi-Z)
EN
IN
OUT
• Transmission gates
0
X
Hi-Z
1
0
0Hale Waihona Puke Baidu
1
1
1
Chapter 2
▪ Exercises:
▪ Two-level circuit optimization
• Karnaugh map (K-map), Prime implicants, essential prime implicants • Simplifying in SOP form (with don’t care conditions) • Cost criteria: gate input cost
▪ Gray Code & ASCII Character Code
Chapter 2
▪ Boolean algebra
• Dual of an algebraic expression: OR<->AND, 0’s <-> 1’s • DeMorgan’s theorem: (X + Y)’ = X’ Y’ and (XY)’ = X’ + Y’ • Identities of Boolean algebra: X+YZ=(X+Y)(X+Z) • Consensus theorem: XY+X’Z+YZ = XY+X’Z, (X+Y)(X’+Z)(Y+Z)=(X+Y)(X’+Z)
• Odd function and even function
▪ Use odd function to generate even parity bit
▪ Use even function to generate odd parity bit
▪ The even function is obtained by replacing the output gate with an
Chapter 1
▪ Conversion between number systems
• Binary number, hexadecimal number
▪ Eg. ( 1101 1111)2 = (DF)16
Decimal
369.3125 189.625 214.625
62407.625
Binary
2).Complement each constant value and literal
• Four variables odd function has __________ “1” squares in its corresponding K-Map.
▪ Complement of a function
▪ Standard forms
• Product terms, sum terms, SOP, POS • Minterms, Maxterms, SOM, POM • Relationship between SOP and SOM? SOM and POM?
• BCD (binary-coded decimal)
▪ Eg. (1001 0101)BCD -> ( 0101 1111)2 -> (5F)16
• Parity Bit
▪ 100 0001 -> 0100 0001 (with even parity) -> 1100 0001 (with odd parity) ▪ How to generate odd parity bit P for any 5-bit binary number D4D3D2D1D0？
101110001.0101 10111101.101 11010110.101 11111.101
Octal
561.24 275.5 326.5
171707.5
Hexadecimal
171.5 BD.A D6.A F3C7.A
▪ Conversion between binary number and decimal code
1. Fill in the blank (20 points, 2pt/per) 2. Multiple Choice (20 points, 2pt/per) 3. Optimization (12 points, 6pt/per) 4. Circuit Analysis (18 points)
• The dual of an algebraic expression is obtained by 1) interchanging OR and AND operations and 2)
replacing 1’s by 0’s and 0’s by 1’s.
• Use DeMorgan's Theorem to complement a function: 1) Interchange AND and OR operators
• Combinational circuit • Sequential circuit
5. Logic Design (30 points)
• Combinational circuit • Sequential circuit
Course Review
HIGHLIGHTS & EXERCISES
LogicandComputerDesignFundamentals
CourseReview
WangDong-hui
Outline
▪ About Final Exam ▪ Highlights & Exercises
Course Review
ABOUT FINAL EXAM
Final Exam