Implement basic logic gates: Not, And, Or, Xor, Mux, DMux

01/And.hdl

@@ -4,12 +4,14 @@
 // File name: projects/1/And.hdl
 /**
  * And gate:
- * if (a and b) out = 1, else out = 0 
+ * if (a and b) out = 1, else out = 0
  */
 CHIP And {
     IN a, b;
     OUT out;
-    
+
     PARTS:
-    //// Replace this comment with your code.
-}
+    // And(a,b) = Not(Nand(a,b))
+    Nand(a=a, b=b, out=nandOut);
+    Not(in=nandOut, out=out);
+}

01/DMux.hdl

@@ -12,5 +12,8 @@ CHIP DMux {
     OUT a, b;
 
     PARTS:
-    //// Replace this comment with your code.
+    // DMux(in,sel) -> a = And(in, Not(sel)), b = And(in, sel)
+    Not(in=sel, out=notSel);
+    And(a=in, b=notSel, out=a);
+    And(a=in, b=sel, out=b);
 }

01/Mux.hdl

@@ -2,7 +2,7 @@
 // and the book "The Elements of Computing Systems"
 // by Nisan and Schocken, MIT Press.
 // File name: projects/1/Mux.hdl
-/** 
+/**
  * Multiplexor:
  * if (sel = 0) out = a, else out = b
  */
@@ -11,5 +11,9 @@ CHIP Mux {
     OUT out;
 
     PARTS:
-    //// Replace this comment with your code.
-}
+    // Mux(a,b,sel) = Or(And(a, Not(sel)), And(b, sel))
+    Not(in=sel, out=notSel);
+    And(a=a, b=notSel, out=aAndNotSel);
+    And(a=b, b=sel, out=bAndSel);
+    Or(a=aAndNotSel, b=bAndSel, out=out);
+}

01/Not.hdl

@@ -11,5 +11,6 @@ CHIP Not {
     OUT out;
 
     PARTS:
-    //// Replace this comment with your code.
+    // Not(in) = Nand(in, in)
+    Nand(a=in, b=in, out=out);
 }

01/Or.hdl

@@ -4,12 +4,16 @@
 // File name: projects/1/Or.hdl
 /**
  * Or gate:
- * if (a or b) out = 1, else out = 0 
+ * if (a or b) out = 1, else out = 0
  */
 CHIP Or {
     IN a, b;
     OUT out;
 
     PARTS:
-    //// Replace this comment with your code.
+    // Or(a,b) = Not(And(Not(a), Not(b))) - De Morgan's law
+    Not(in=a, out=notA);
+    Not(in=b, out=notB);
+    And(a=notA, b=notB, out=andOut);
+    Not(in=andOut, out=out);
 }

01/Xor.hdl

@@ -11,5 +11,10 @@ CHIP Xor {
     OUT out;
 
     PARTS:
-    //// Replace this comment with your code.
-}
+    // Xor(a,b) = Or(And(a, Not(b)), And(Not(a), b))
+    Not(in=a, out=notA);
+    Not(in=b, out=notB);
+    And(a=a, b=notB, out=aAndNotB);
+    And(a=notA, b=b, out=notAAndB);
+    Or(a=aAndNotB, b=notAAndB, out=out);
+}