diff --git a/book/src/design/circuit/gadgets/decomposition.md b/book/src/design/circuit/gadgets/decomposition.md
index 2cdcaae8..d65e4b13 100644
--- a/book/src/design/circuit/gadgets/decomposition.md
+++ b/book/src/design/circuit/gadgets/decomposition.md
@@ -11,7 +11,10 @@ z_1 &= (z_0 - k_0) / 2^K \\
     &= k_1 + 2^{K} \cdot k_2 +  2^{2K} \cdot k_3 + \cdots, \\
 z_2 &= (z_1 - k_1) / 2^K \\
     &= k_2 +  2^{K} \cdot k_3 + \cdots, \\
-    &\vdots
+    &\vdots \\
+\downarrow &\text{ (in strict mode)} \\
+z_W &= (z_{W-1} - k_{W-1}) / 2^K \\
+    &= 0 \text{ (because } z_{W-1} = k_{W-1} \text{)}
 \end{aligned}
 $$
 
diff --git a/book/src/design/circuit/gadgets/ecc/fixed-base-scalar-mul.md b/book/src/design/circuit/gadgets/ecc/fixed-base-scalar-mul.md
index fe20fb93..c5388a39 100644
--- a/book/src/design/circuit/gadgets/ecc/fixed-base-scalar-mul.md
+++ b/book/src/design/circuit/gadgets/ecc/fixed-base-scalar-mul.md
@@ -19,7 +19,7 @@ $$
 \begin{array}{|c|l|}
 \hline
 \text{Degree} & \text{Constraint} \\\hline
-9 & q_\text{scalar-fixed} \cdot 1 \cdot \left(\sum\limits_{i=0}^7{w - i}\right) = 0 \\\hline
+9 & q_\text{scalar-fixed} \cdot \left(\sum\limits_{i=0}^7{w - i}\right) = 0 \\\hline
 \end{array}
 $$