diff --git a/00/Off.hdl b/00/Off.hdl
index 9d6b464..6377855 100755
--- a/00/Off.hdl
+++ b/00/Off.hdl
@@ -13,7 +13,6 @@ CHIP Off {
     OUT out;
 
     PARTS:
-    // Put your code here:
-    // Nand(a=true, b=false, out=out);  // old
+    // always output false
     Nand(a=true, b=true, out=out);
 }
diff --git a/01/And.hdl b/01/And.hdl
index ada4be7..c78b333 100644
--- a/01/And.hdl
+++ b/01/And.hdl
@@ -11,7 +11,7 @@ CHIP And {
     OUT out;
 
     PARTS:
-    // And = Not(Nand)
+    // Nand = Not(Nand), so And = Not(Nand)
     Nand(a=a, b=b, out=tmp);
     Not(in=tmp, out=out);
 }
diff --git a/01/DMux.hdl b/01/DMux.hdl
index dfe0b1e..e47b62b 100644
--- a/01/DMux.hdl
+++ b/01/DMux.hdl
@@ -12,7 +12,10 @@ CHIP DMux {
     OUT a, b;
 
     PARTS:
-    Not(in=sel, out=tmp);
-    And(a=in, b=tmp, out=a);
+    // invert sel
+    Not(in=sel, out=notSel);
+    // when sel=0: a gets in
+    And(a=in, b=notSel, out=a);
+    // when sel=1: b gets in
     And(a=in, b=sel, out=b);
 }
diff --git a/01/DMux4Way.hdl b/01/DMux4Way.hdl
index 70028d6..ec2d0ff 100644
--- a/01/DMux4Way.hdl
+++ b/01/DMux4Way.hdl
@@ -14,7 +14,9 @@ CHIP DMux4Way {
     OUT a, b, c, d;
 
     PARTS:
-    DMux(in=in, sel=sel[1], a=tmp1, b=tmp2);
-    DMux(in=tmp1, sel=sel[0], a=a, b=b);
-    DMux(in=tmp2, sel=sel[0], a=c, b=d);
+    // sel[1] split in to two groups
+    DMux(in=in, sel=sel[1], a=lowGroup, b=highGroup);
+    // sel[0] split each group to out
+    DMux(in=lowGroup, sel=sel[0], a=a, b=b);
+    DMux(in=highGroup, sel=sel[0], a=c, b=d);
 }
diff --git a/01/DMux8Way.hdl b/01/DMux8Way.hdl
index b598823..bfe3022 100644
--- a/01/DMux8Way.hdl
+++ b/01/DMux8Way.hdl
@@ -18,7 +18,9 @@ CHIP DMux8Way {
     OUT a, b, c, d, e, f, g, h;
 
     PARTS:
-    DMux(in=in, sel=sel[2], a=tmp1, b=tmp2);
-    DMux4Way(in=tmp1, sel=sel[0..1], a=a, b=b, c=c, d=d);
-    DMux4Way(in=tmp2, sel=sel[0..1], a=e, b=f, c=g, d=h);
+    // sel[2] split in to two groups of 4
+    DMux(in=in, sel=sel[2], a=lowGroup, b=highGroup);
+    // sel[0..1] split each group to out
+    DMux4Way(in=lowGroup, sel=sel[0..1], a=a, b=b, c=c, d=d);
+    DMux4Way(in=highGroup, sel=sel[0..1], a=e, b=f, c=g, d=h);
 }
diff --git a/01/Mux.hdl b/01/Mux.hdl
index 422cae7..bce60f4 100644
--- a/01/Mux.hdl
+++ b/01/Mux.hdl
@@ -11,8 +11,12 @@ CHIP Mux {
     OUT out;
 
     PARTS:
-    Not(in=sel, out=tmp1);
-    And(a=a, b=tmp1, out=tmp2);
-    And(a=b, b=sel, out=tmp3);
-    Or(a=tmp2, b=tmp3, out=out);
+    // invert selector
+    Not(in=sel, out=notSel);
+    // when sel=0: aPath gets a
+    And(a=a, b=notSel, out=aPath);
+    // when sel=1: bPath gets b
+    And(a=b, b=sel, out=bPath);
+    // combine both paths
+    Or(a=aPath, b=bPath, out=out);
 }
diff --git a/01/Mux4Way16.hdl b/01/Mux4Way16.hdl
index 8b62e8f..92ec13c 100644
--- a/01/Mux4Way16.hdl
+++ b/01/Mux4Way16.hdl
@@ -14,7 +14,9 @@ CHIP Mux4Way16 {
     OUT out[16];
 
     PARTS:
-    Mux16(a=a, b=b, sel=sel[0], out=tmp1);
-    Mux16(a=c, b=d, sel=sel[0], out=tmp2);
-    Mux16(a=tmp1, b=tmp2, sel=sel[1], out=out);
+    // sel[0] pick from each group
+    Mux16(a=a, b=b, sel=sel[0], out=lowGroup); // group ab
+    Mux16(a=c, b=d, sel=sel[0], out=highGroup); // group cd
+    // sel[1] pick which group
+    Mux16(a=lowGroup, b=highGroup, sel=sel[1], out=out);
 }
diff --git a/01/Mux8Way16.hdl b/01/Mux8Way16.hdl
index 57c541b..2173699 100644
--- a/01/Mux8Way16.hdl
+++ b/01/Mux8Way16.hdl
@@ -20,7 +20,9 @@ CHIP Mux8Way16 {
     OUT out[16];
 
     PARTS:
-    Mux4Way16(a=a, b=b, c=c, d=d, sel=sel[0..1], out=tmp1);
-    Mux4Way16(a=e, b=f, c=g, d=h, sel=sel[0..1], out=tmp2);
-    Mux16(a=tmp1, b=tmp2, sel=sel[2], out=out);
+    // sel[0..1] pick from each group
+    Mux4Way16(a=a, b=b, c=c, d=d, sel=sel[0..1], out=lowGroup); // group abcd
+    Mux4Way16(a=e, b=f, c=g, d=h, sel=sel[0..1], out=highGroup); // group efgh
+    // sel[2] pick which group
+    Mux16(a=lowGroup, b=highGroup, sel=sel[2], out=out);
 }
diff --git a/01/Or8Way.hdl b/01/Or8Way.hdl
index 498820e..83cdfc7 100644
--- a/01/Or8Way.hdl
+++ b/01/Or8Way.hdl
@@ -11,11 +11,14 @@ CHIP Or8Way {
     OUT out;
 
     PARTS:
-    Or(a=in[0], b=in[1], out=tmp1);
-    Or(a=in[2], b=in[3], out=tmp2);
-    Or(a=in[4], b=in[5], out=tmp3);
-    Or(a=in[6], b=in[7], out=tmp4);
-    Or(a=tmp1, b=tmp2, out=tmp5);
-    Or(a=tmp3, b=tmp4, out=tmp6);
-    Or(a=tmp5, b=tmp6, out=out);
+    // combine pairs
+    Or(a=in[0], b=in[1], out=pair0);
+    Or(a=in[2], b=in[3], out=pair1);
+    Or(a=in[4], b=in[5], out=pair2);
+    Or(a=in[6], b=in[7], out=pair3);
+    // combine groups of pairs
+    Or(a=pair0, b=pair1, out=lowGroup);
+    Or(a=pair2, b=pair3, out=highGroup);
+    // combine both groups
+    Or(a=lowGroup, b=highGroup, out=out);
 }
diff --git a/01/Xor.hdl b/01/Xor.hdl
index c6229a8..ad4dacd 100644
--- a/01/Xor.hdl
+++ b/01/Xor.hdl
@@ -11,9 +11,13 @@ CHIP Xor {
     OUT out;
 
     PARTS:
-    Not(in=a, out=tmp1);
-    Not(in=b, out=tmp2);
-    And(a=a, b=tmp2, out=tmp3);
-    And(a=tmp1, b=b, out=tmp4);
-    Or(a=tmp3, b=tmp4, out=out);
+    // invert both inputs
+    Not(in=a, out=notA);
+    Not(in=b, out=notB);
+    // a and not b path
+    And(a=a, b=notB, out=aPath);
+    // not a and b path
+    And(a=notA, b=b, out=bPath);
+    // combine both paths
+    Or(a=aPath, b=bPath, out=out);
 }
diff --git a/01/chapter1lecture.pdf b/01/chapter1lecture.pdf
deleted file mode 100644
index cf0d9f2..0000000
Binary files a/01/chapter1lecture.pdf and /dev/null differ