Quizzes

约 450 个字 预计阅读时间 2 分钟

Quiz 1

1. Represent the decimal number 75 as a 7-bit binary number: ( 1 ), and as a BCD code: ( 2 ). Then add an even parity bit at the most significant bit (MSB) of the BCD code to form a 9-bit code: ( 3 ).

2. Simplify the Boolean expression \(XY + \bar{X}Z + X\bar{Y} + \bar{Y}Z\) to its minimum number of literals:

   • A: \(Y + Z\)
   • B: \(X + Z\)
   • C: \(X + Y\)
   • D: \(X + Y + Z\)

3. Which of the following expressions has its dual equal to its complement?

   • A: \(\bar{A} + BC\)
   • B: \(\bar{A}B + BC\)
   • C: \(\bar{A}\bar{B} + BC\)
   • D: \(\bar{A}B + A\bar{B}\)

4. What is the sum-of-minterms (SOM) form of the expression \(F(A,B,C) = \bar{A}B + BC\)?

   • A: \(\sum m(2,3,7)\)
   • B: \(\sum m(0,1,4)\)
   • C: \(\sum m(2,4,6)\)
   • D: \(\sum m(2,3,6)\)

Answer

1. As below:

   • Binary Code: \(1001011_2\)
     • \(75 = 64 + 11\)
   • BCD Code: \(0111\ 0101\)
   • 9-bit Code (Even Parity): \(1\ 0111\ 0101\)

2. B (\(X + Z\))

3. D (\(\bar{A}B + A\bar{B}\))
   • \(f^D(x, y, z) = \bar{f}(x, y, z) = f^D(\bar{x}, \bar{y}, \bar{z}) \Longleftrightarrow f(x, y, z) = f(\bar{x}, \bar{y}, \bar{z})\)
4. A (\(\sum m(2,3,7)\))

Quiz 2

1. For the function \(F = AB(C+D)+C(BD'+\bar{A}D)\), the literal cost is: ( 1 ), and the gate input cost with NOT (GN) is: ( 2 ).

2. Find the essential prime implicants for \(F(W,X,Y,Z)= \sum m(0,1,4,6,7,8,9,12,14,15)\):

   • A: \(Y'Z', XZ'\)
   • B: \(\bar{X}\bar{Y}, XY\)
   • C: \(XY, XZ'\)
   • D: \(Y'Z', \bar{X}\bar{Y}\)

3. Find a minimal sum-of-products (SOP) expression for the function \(F\) with the don’t-care conditions: \(F(A,B,C,D)=\sum m(1,5,6,13,14)+ \sum d(4,12)\):

   • A: \(B\bar{C}+\bar{A}\bar{C}D+BCD'\)
   • B: \(B\bar{D}+B\bar{C}+\bar{A}\bar{C}\)
   • C: \(\bar{C}D+B\bar{C}+B\bar{D}\)
   • D: \(B\bar{C}+B\bar{D}+\bar{A}\bar{C}D\)

4. How many implicants, prime implicants (PI), and essential prime implicants (EPI) are there in \(F(A,B,C)=\sum m(0,4,5)+ \sum d(1)\)?

   • A: 8, 1, 1
   • B: 7, 1, 1
   • C: 6, 1, 1
   • D: 5, 3, 1

Answer

1. As below:

   • Literal cost: 9
   • Gate input cost with NOT (GN): 17

2. B (\(\bar{X}\bar{Y}, XY\))

3. D (\(B\bar{C}+B\bar{D}+\bar{A}\bar{C}D\))
4. A (8, 1, 1)
   • Implicants: 3 + 4 + 1 = 8.
   • PI/EPI: Combined term \(\bar{C}\) covers all required minterms.

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