Homework #1
Winter 2013
ECE15a
1.
(a)
For the whole part, we simply convert it to binary using a sequence of division by 2.
Therefore, 17 = (00010001)2.
For the fractional part, we begin with the decimal fraction and multiply by 2. The whole
number part o
Homework #1
due January 23 at noon
Winter 2013
ECE 15a
1. Do the following conversion problems:
(5p) (a) Convert decimal 17.2125 to binary. Assume that the integral and fractional parts of the
number can use 8 bits each.
(5p) (b) Calculate the binary equi
Homework #2
due January 28 at noon
ECE 15a
Winter 2013
On your homework, please, write the day and time of your discussion section.
For problems 1-4, assume the 2-value Boolean algebra over the set B=cfw_0,1 with + and . operators defined as:
+ 01
0 01
1
Homework #3
due February 4 at noon
ECE 15a
Winter 2013
On your homework, please, write your discussion section day and time.
1. Express each of the following functions in disjunctive normal form*
(DNF) in the smallest possible number of variables:
(2p) (a
Homework #4
due February 11 at noon
ECE 15a
Winter 2013
On your homework, please, write your discussion section day and time.
(2p) 1. Draw a Venn diagrams illustrating the a b and a b operations.
2. Write the following functions using only + (OR), (AND) a
ECE 15a
Winter 2013
Homework #5
Due Wednesday, February 20 at noon
1. (10p) For this function, find a minimum sum-of-products solution, using the
Quine-McCluskey method:
F(a,b,c,d,e) = m (0,2,3,7,8,9,10,12,15,18, 19,31) + d(4,13,23)
2. (10p) Find all prim
Homework #6
due February 25 at noon
ECE 15a
Winter 2013
1. Implement f(a,b,c,d) =
gates.
m(0,1,3,4,5,6,7,11,15) as a2-level gate circuit, using a minimum number of
(3p) (a) Use AND and NAND gates.
(3p) (b) Use NAND gates only.
2. Convert the circuit show
Homework #6
ECE 15a Winter 2013
1. Implement f(a,b,c,d) = m(0,1,3,4,5,6,7,11,15) as a 2-level gate circuit, using a minimum number of
gates.
(3p) (a) Use AND and NAND gates.
(3p) (b) Use NAND gates only.
Solution:
The K-Map of this function is as follows:
Homework #7
due March 4 at noon
ECE 15a
Winter 2013
1. (15p) Design a combinational circuit with four inputs, x,y,w, and z, and four outputs: A, B, C, and D.
When the binary input value in decimal is 3,8,12 or 15, the binary output value is one less than
Homework #8
due March 11 at noon
ECE 15a
Winter 2013
(5p)1. Build the 8-to-3 priority encoder using two 4-to-2 priority encoders, one 2-to-1 priority encoder
and 2-to-1 MUXes.
(5p) 2. A combinational circuit is defined by the following three Boolean funct