Quizzes¶

约 669 个字 3 张图片预计阅读时间 2 分钟

Quiz 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 ).
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: $X + Y + Z$
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: $\bar{A}B + A\bar{B}$
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

As below:
- Binary Code: $1001011_2$
  - $75 = 64 + 11$
- BCD Code: $0111\ 0101$
- 9-bit Code (Even Parity): $1\ 0111\ 0101$
B ($X + Z$)
D ($\bar{A}B + A\bar{B}$)
- $f^D(x, y, z) = \bar{f}(x, y, z) = f^D(\bar{x}, \bar{y}, \bar{z}) \Longleftrightarrow f(x, y, z) = f(\bar{x}, \bar{y}, \bar{z})$
A ($\sum m(2,3,7)$)

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 ).
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: $Y'Z', \bar{X}\bar{Y}$
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: $B\bar{C}+B\bar{D}+\bar{A}\bar{C}D$
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

As below:
- Literal cost: 9
- Gate input cost with NOT (GN): 17
B ($\bar{X}\bar{Y}, XY$)
D ($B\bar{C}+B\bar{D}+\bar{A}\bar{C}D$)
A (8, 1, 1)
- Implicants: 3 + 4 + 1 = 8.
- PI/EPI: Combined term $\bar{C}$ covers all required minterms.

Find the $t_\text{PHL}$ from input C to the output D, assuming $t_\text{PHL}=0.20\text{ ns}$ and $t_\text{PLH}=0.36\text{ ns}$ for each gate.
- A: 0.56 ns
- B: 0.6 ns
- C: 0.76 ns
- D: 0.92 ns
Consider a 4-input priority encoder with inputs $D_3$, $D_2$, $D_1$, $D_0$. The encoder responds to the most significant 1 (highest priority to $D_3$). It produces outputs $A_1$, $A_0$ and a valid flag $V$, where $V=1$ indicates at least one input is 1. What is the logic expression for $V$?
- A: $D_3D_2 + D_1D_0$
- B: $D_3D_2 + D_1 + D_0$
- C: $D_3D_2D_1 + D_0$
- D: $D_3 + D_2 + D_1 + D_0$
Please find the logic expression of output $F$ in the figure.
- A: $XY + X\bar{Y}$
- B: $\bar{X}\bar{Y} + XY$
- C: $\bar{X}Y + XY$
- D: $\bar{X}Y + X\bar{Y}$
What specific Boolean function does the PLA implement for $F_2$?
- A: $AC + BC$
- B: $\bar{C}+\bar{A}\bar{B}$
- C: $\bar{A}C + BC$
- D: $AC + B$

Answer