diff --git a/plonky2/src/gates/base_sum.rs b/plonky2/src/gates/base_sum.rs
index a7f4fcb3..5be54eeb 100644
--- a/plonky2/src/gates/base_sum.rs
+++ b/plonky2/src/gates/base_sum.rs
@@ -3,6 +3,7 @@ use std::ops::Range;
 use plonky2_field::extension::Extendable;
 use plonky2_field::packed::PackedField;
 use plonky2_field::types::{Field, Field64};
+use plonky2_util::log_floor;
 
 use crate::gates::gate::Gate;
 use crate::gates::packed_util::PackedEvaluableBase;
@@ -32,7 +33,8 @@ impl<const B: usize> BaseSumGate<B> {
     }
 
     pub fn new_from_config<F: Field64>(config: &CircuitConfig) -> Self {
-        let num_limbs = F::BITS.min(config.num_routed_wires - Self::START_LIMBS);
+        let num_limbs =
+            log_floor(F::ORDER - 1, B as u64).min(config.num_routed_wires - Self::START_LIMBS);
         Self::new(num_limbs)
     }
 
diff --git a/util/src/lib.rs b/util/src/lib.rs
index 61677ff0..bbc2af98 100644
--- a/util/src/lib.rs
+++ b/util/src/lib.rs
@@ -38,6 +38,23 @@ pub fn log2_strict(n: usize) -> usize {
     res as usize
 }
 
+/// Returns the largest integer `i` such that `base**i <= n`.
+pub const fn log_floor(n: u64, base: u64) -> usize {
+    assert!(n > 0);
+    assert!(base > 1);
+    let mut i = 0;
+    let mut cur: u64 = 1;
+    loop {
+        let (mul, overflow) = cur.overflowing_mul(base);
+        if overflow || mul > n {
+            return i;
+        } else {
+            i += 1;
+            cur = mul;
+        }
+    }
+}
+
 /// Permutes `arr` such that each index is mapped to its reverse in binary.
 pub fn reverse_index_bits<T: Copy>(arr: &[T]) -> Vec<T> {
     let n = arr.len();