Hardware Quiz 1

1. As her Christmas gift, Joyce received a toy doll with a small computer chip embedded. When she presses the tummy of the doll, it says "Hello, Joyce!"; when she presses again, it says "Merry Christmas!"; on the next press, it says "I love you!"; and whenever Joyce presses twice quickly, it says "Good-bye!".

Which of the following statements about the doll are correct? Check all that apply.

the chip is a synchronous system

the chip contains memory elements

the chip can recongize two different inputs

the chip is a combinational system


2. Bob is designing a digital system to implement the multiplication table. When two single-digit integers (0-9), e.g. 4 and 7, are entered, the system will output their product (28 in this case). When both input and output are expressed in binary, the system should have 8 bits as input (4 bits for each number) and 7 bits as output (the largest output is 81 and needs no more than 7 bits).

There are 2^8 = 256 combinations for the 8 input bits. However, for the multiplication table, there will be only 100 entries (axb with both a and b go from 0 to 9). So there will be 256-100 = 156 don't care conditions.

Please enter 1 to show that you have understood this and earn the point :)




3. Which of the following gate(s) are universal? Check all that apply.

hint: A universal gate should be able to implement {AND, OR, NOT}

{OR, NOT}

NAND

XOR

{AND, OR}


4. For the 3-input gate f(x,y,z)=x′yz+xy′+y′z, what is the value of f(x,0,1)?

0

none of the others

x'

1

x


5. f(x,y,z) is a 3-input 2-output function. How many different f(x,y,z) can we have to make f(0,0,1)=01,f(0,1,0)=10,f(1,0,0)=11 ?

(hint: Two functions are different if there is an input combination on which the two functions give different output. Think about what could be the output of f on each of the input combinations other than the 3 specified cases).

1024


6. For the four 2-input logic gates (NAND, NOR, XOR, XNOR), each with x and y as their inputs, which of the following statements about observability don't care (ODC) are true? Check all that apply. (If you forget the definition of these standard logic gates, you can find them in the slide "Example: System Implementation").

when y=0, x input is ODC for NAND gate

when y=0, x input is ODC for XOR gate

when x=0, y input is ODC for NOR gate

there is no ODC for XNOR gate


7. Consider the following two functions, S and C, defined on three inputs x, y, z: S(x,y,z)=x⊕y⊕z, C(x,y,z)=x∙y+z∙(x⊕y), where ⊕ is the XOR gate, + is the OR gate, and ∙ is the AND gate.
Which of the following conditions are satisfiability don't cares? Check all that apply.

x=1, y=1, z=0, C=1

x=0, y=0, z=1, S=0

x=1, y=1, z=1, S=1

x=0, z=0, C=1