homework_01 with solution

Homework 1
1. (1pt) Convert the hexadecimal number 9D7A4 to base 7
5324356

2. (1.5pts) Logic and Gate
1) Draw a table of negative implementation for AND gate
A
H
L
H
L

B
H
H
L
L

AND
H
H
H
L

2) Draw a table of positive logic implementation for OR gate
A
L
L
H
H

B
L
H
L
H

OR
L
H
H
H

3) Are 1) and 2) are equivalent?
Yes, they are equivalent.

3. (3.5pts) consider the logic gate circuit shown below

1) Derive a Boolean equation for the output X
X = a * c + b + a*c

2) Draw a truth table for the circuit a 0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1

b
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1

c
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1

d
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1

X
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1

4. (1pt) Introduction to Logisim
See attachment, Q4.circ

5. (3pts) Simulation and testing an ALU circuit
1) Simulate this ALU with Logisim, and save the circuit file.
See attachment, Q5.circ

2) Based on the signal change of F0, F1, see how the output changes based on A and B signals. Make a truth table (A, B, carry in as inputs: output and carry out as output ) for each case, and infer what is the operation for each case.
Truth table:
CarryIn
0

A
0

B
0

F0
0

F1
0

Output
0

CarryOut
0

0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1