Download The solution to Homework Assignment #0

Homework Assignment #0
EE 477 Spring 2014 Professor Parker
1) Give a Boolean expression for the detection of overflow in addition of two binary numbers in
terms of specific bits of the numbers. The numbers are each 8 bits with one bit being the sign
bit, in 2's complement form
c8 c7 c6 c5 c4 c3 c2 c1 c0
a8 a7 a6 a5 a4 a3 a2 a1
b8 b7 b6 b5 b4 b3 b2 b1
We can detect overflow with an XOR function with inputs c8 and c7
Each position i of the carry is defined by
ci = Gi + ci −1Pi ;
Gi = aibi
Pi = ai ⊕ bi
c8 = G8 + c7 P8 ;
G8 = a8b8
P8 = a8 ⊕ b8
c7 = G7 + c6 P7 ;
G7 = a7b7
P7 = a7 ⊕ b7
(refer to hw#1 solution Fall 2012 for more details)
c8 = a8b8 +P8 (G7 + G6 P7 + G5 P7 P6 + G4 P7 P6 P5 + G3 P7 P6 P5 P4 + G2 P7 P6 P5 P4 P3 + G1P7 P6 P5 P4 P3 P2 + c0 P7 P6 P5 P4 P3 P2 P1 )
c7 = a7b7 +P7 (G6 + G5 P6 + G4 P6 P5 + G3 P6 P5 P4 + G2 P6 P5 P4 P3 + G1P6 P5 P4 P3 P2 + c0 P6 P5 P4 P3 P2 P1 )
Since the input carry is 0, we can neglect the last term.
c8 = a8b8 +P8 (G7 + G6 P7 + G5 P7 P6 + G4 P7 P6 P5 + G3 P7 P6 P5 P4 + G2 P7 P6 P5 P4 P3 + G1 P7 P6 P5 P4 P3 P2 )
c7 = a7b7 +P7 (G6 + G5 P6 + G4 P6 P5 + G3 P6 P5 P4 + G2 P6 P5 P4 P3 + G1P6 P5 P4 P3 P2 )
P8 = a8 ⊕ b8
P7 = a7 ⊕ b7
P6 = a6 ⊕ b6
P5 = a5 ⊕ b5
P4 = a4 ⊕ b4
P3 = a3 ⊕ b3
P2 = a2 ⊕ b2
P1 = a1 ⊕ b1
Overflow_detection= c8 ⊕ c7
2) Show the representation of two numbers, -9 and 11 in 2's complement form. Use the least
number of bits required for this.
− 9 → 10111
11 → 01011
3) Write the Boolean function for a full adder.
x
0
0
0
0
1
1
1
1
y
0
0
1
1
0
0
1
1
z
0
1
0
1
0
1
0
1
C
0
0
0
1
0
1
1
1
S
0
1
1
0
1
0
0
1
S = x' y ' z + x' yz '+ xy ' z '+ xy ' z '+ xyz
C = xy + xz + yz = xy + xy ' z + x' yz
4) Implement the Boolean equation Z = ABC + DEF using only AND gates and inverters.
5) What is the total area of a rectangle that is 0.090 nanometers x 1200 femtometers?
(.090x10 )(1200x10 ) = 108x10
−9
−15
−24
6) Two capacitors are in series. One is 55 fF and one is 54 fF. What is the total capacitance?
C = 27.2 fF
7) What is the relationship between current and voltage in a capacitor?
i (t ) = C dV
V=
dt
1
∫ i (t )dt
C
8) State Kirchoff's current law and voltage law.
n
∑I
k =1
k
n
∑V
k =1
k
=0
=0
Iks are all the currents entering a node, and the Vks and the voltages in a closed loop in a circuit
9) The best way to store charge is a) resistor b) capacitor c) inductor?
Capacitor
10) A 14 ohm resistor is in parallel with a 7 ohm resistor. What is the total resistance?
R = 4.7Ω