Homework 1 Due 21st May 2014

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

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 = 3 + 3 + 3

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

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

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 = 3 + 3 + 3 + 4