logic and computer design quiz 2

Given the following diagram, what's the maximum number of states represented by this sequential diagram.

Correct Answer:      4


Number (10101010)2 is in signed-magnitude representation. What is this number on signed 2s complement representation?

 Answer: 11010110



What is the result of the following subtraction:
-69-15
Assume 8-bit signed 2s complement numbers.
 Answer: c. 10101100


The following truth table represents the formulation of a circuit to convert 3-bit gray code to binary code. What are the inputs for the dual 4-to-1 MUX implementation of outputs Y and Z as seen below? (listed in order from D00 to D03).
Gray Binary
A B C X Y Z
0 0 0 0 0 0
1 0 0 0 0 1
1 1 0 0 1 0
0 1 0 0 1 1
0 1 1 1 0 0
1 1 1 1 0 1
1 0 1 1 1 0
0 0 1 1 1 1

 Answer:     c. Y Mux: C, ~C, C, ~C Z Mux: C,~C,~C,C

Which of the following options result in overflow (in 2s complement with 8-bit).
 Answer: b. 10111010 + 10110001




Given the following circuit what is the correct equation for D A?

Answer:     b. DA=XB+YA

For a one bit full-adder, X and Y are two bits to be added, and Z is the carry in from the previous lower significant position. What's the equation for carry cout Cout?
Answer
Selected Answer: d. Cout(X, Y, Z) = Σm(3, 5, 6, 7)


Given a half adder whose sum is expressed as a sum bit S and a carry bit C, which of the following is an incorrect equation for the half adder?
Answer
Answer: e. S= (~X+Y)+(X+Y) C=XY



  Given that a state diagram has 2 inputs and 6 states (outputs can be ignored), what is the largest number of arcs that will appear in the entire diagram (not just on one state)?
Answer
 Answer: b. 24




What is the minimum number of flip-flops that you may need for the sequential circuit that may have 209 different states?
Answer
Correct Answer: 8


Given the following function F and don't care conditions, what's the simplification form of F?
F(A ,B, C, D) = Σm(3, 4, 13, 15)
d(A, B, C, D) = Σm(2, 5, 8, 10, 12, 14)
Answer
Answer: c. B~C + AB + ~A~BC


What is the minimum number of outputs that encoder with 145 inputs should have?
Answer
 Answer: 8
Answer range +/- 0 (8 - 8)



What is the indication of overflow when adding two 2s complement encoded numbers?
Answer
Answer: a. the carry into the sign bit position and the carry out of the sign bit postion are not equal


Which of the following hexadecimal numbers are representable by 8-bit 2s complement.
Answer
 Answers: b. -80



With signed numbers, overflow cannot occur for an addition of two negative numbers.
Answer
Answer: False


 How many different signed integers can be represented with 16 bits using 2s complement representation?
Answer
Answer: a. 216


 What is the literal cost of the following equation:
F = (AB) + (CD~E) + (~A~B~C)
Answer
Answer: c. 8

How many D flip-flops at least do you need to construct a sequential circuit with 5 states, 3 inputs and 1 output?
Answer
 Answer: b. 3