form-f-x-y-z-xy-c-x-c-y-z-in-standard-SOP-form-and-canonical-SOP-form-

Question Number 157725 by joki last updated on 27/Oct/21

form f (x, y, z) = {({(xy)}^{'} c)}^{'} {((x^{'} + c) (y^{'} + z^{'}))}^{'}

in standard SOP form and canonical SOP form

Answered by Kunal12588 last updated on 27/Oct/21

{[{(x y)}^{'} c]}^{'} {[(x^{'} + c) (y^{'} + z^{'})]}^{'}

= [{({(x y)}^{'})}^{'} + c^{'}] [{(x^{'} + c)}^{'} + {(y^{'} + z^{'})}^{'}]

= (x y + c^{'}) ({x c}^{'} + y z)

= {x y c}^{'} + x y z + {x c}^{'} + {y z c}^{'}

= {x c}^{'} (y + 1) + x y z + {y z c}^{'}

S S O P = {x c}^{'} + x y z + {y z c}^{'}

C S O P = {x c}^{'} (y + y^{'}) (z + z^{'}) + x y z (c + c^{'}) + {y z c}^{'} (x + x^{'})

= {x y z c}^{'} + {x y z}^{'} c^{'} + {x y}^{'} {z c}^{'} + {x y}^{'} z^{'} c^{'} + x y z c + x^{'} {y z c}^{'}