1. Homework 1
Due 21st May 2014

2. Prove the Dual of the following Consensus Theorem
x.y + x’.z + y.z = x.y + x’.z
Marks = 6

3. Note: The legend for the aforementioned symbols is as follows
Prove whether the following Associativity Relationships are correct or incorrect?
a ^ (b ^ c) = (a ^ b) ^ c
a (b c) = (a b) c
a (b c) = (a b) c
Note: The legend for the aforementioned symbols is as follows ^
XOR
NAND
NOR
Marks =

4. Convert the following SOP expression into a POS expression
f = x.y + x’.y.z’ + y’.z’
Convert the following POS expression into a SOP expression
f = ( x + y ).( x’ + y + z’ ).( y’ + z’ )
Marks = 3 + 3

5. Convert the following SOP expression into a C-SOP expression
f = x.y + x’.y.z’ + y’.z’
Convert the following POS expression into a C-POS expression
f = ( x + y ).( x’ + y + z’ ).( y’ + z’ )
Marks = 3 + 3

6. Implement This Function using
two 8-to-1 Line Multiplexers
two 4-to-1 Line Multiplexers
two 2-to-1 Line Multiplexers
two 8-to-1 Line Multiplexer s (where the Multiplexers are tree structures of smaller multiplexers)
Marks =