For each of the following circuits determine if the output w

For each of the following circuits, determine if the output will be 1 for an odd number of 1 inputs or 1 for an even number of 1 inputs.

Solution

F1= (A^B)\'^(C^D)\'

ABCD=1010(even no of 1\'s)

(1^0)\'^(1^0)\'=0^0=0

ABCD=1101(odd no of1\'s)

(1^1)\'^(0^1)\'=1^0=1

so F1 produce output when theres is odd no of1\'s

b)

F2=((w^x)^(y^z))\'

wxyz=1010(even no of 1\'s)

F2=((1^0)^(1^0))\'=(1^1)\'=1

wxyz=1110(odd no of1\'s)

F2=((1^1)^(1^0))\'=(0^1)\'=0

F2 will prodec output as 1 for even no of 1\'s

c)

F3=((A^B)\'^(C^D))\'^(E^F)\'

For ABCDEF=101011(For even no of 1\'s)

F3=((1^0)\'^(1^0))\'^(1^1)\'

=(0^1)\'^1=0^1=1

For ABCDEF=101010(For odd no of 1\'s)

F3=((1^0)\'^(1^0))\'^(1^0)\'

=0^0=0

F3 will produce output 1 for even numbers of 1 as input