Boolean Logic : Activity 6

Activity 6 : Build MUX by using (NAND, OR, AND, NOT)


Write truth table -> canonical form 

/**
 * Multiplexor. If sel==1 then out=b else out=a.
 */

CHIP Mux {
    IN a, b, sel;
    OUT out;

    PARTS:
    // Put your code here.
    Not(in=a, out=nota);
    Not(in=b, out=notb);
    Not(in=sel, out=notsel);


    And(a=nota, b=b, out=a1);
    And(a=a, b=b, out=a2);
    Or(a=a1, b=a2, out=o1);
    And(a=sel, b=o1, out=p1);

    And(a=a, b=notb, out=a3);
    Or(a=a2, b=a3, out=o2);
    And(a=notsel, b=o2, out=p2);


    Or(a=p1, b=p2, out=out);
}

On simplifying further :

way 2 >

/** 

 * Multiplexor. If sel==1 then out=b else out=a.

 */

CHIP Mux {

    IN a, b, sel;

    OUT out;

    PARTS:

    // Put your code here.

    Not(in=a, out=nota);

    Not(in=b, out=notb);

    Not(in=sel, out=notsel);

    And(a=a, b=b, out=a3);

    And(a=nota, b=b, out=t1);

    And(a=t1, b=sel, out=a1);

    And(a=a, b=notb, out=t2);

    And(a=t2, b=notsel, out=a2);

    Or(a=a1, b=a2, out=o1);

    Or(a=o1, b=a3, out=out);

}

Both the above solutions were built sequentially. Now its time to shorten it.. 

way 3>

/** 

 * Multiplexor. If sel==1 then out=b else out=a.

 */

CHIP Mux {

    IN a, b, sel;

    OUT out;

    PARTS:

    // Put your code here.

    Not(in=sel, out=notsel);

    And(a=a, b=notsel, out=w1);

    And(a=b, b=sel, out=w2);

    Or(a=w1, b=w2, out=out);

}

Downloads : 

activity 6

activity 6 | way 2

activity 6 | way 3