diff --git a/src/fri/recursive_verifier.rs b/src/fri/recursive_verifier.rs
index 6c245167..81cc59ab 100644
--- a/src/fri/recursive_verifier.rs
+++ b/src/fri/recursive_verifier.rs
@@ -49,7 +49,7 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         inputs.push(proof.pow_witness);
 
         let hash = self.hash_n_to_m(inputs, 1, false)[0];
-        self.assert_trailing_zeros(hash, config.proof_of_work_bits);
+        self.assert_trailing_zeros::<64>(hash, config.proof_of_work_bits);
 
         Ok(())
     }
diff --git a/src/gadgets/split_base.rs b/src/gadgets/split_base.rs
index e622be75..35d5ac93 100644
--- a/src/gadgets/split_base.rs
+++ b/src/gadgets/split_base.rs
@@ -11,23 +11,85 @@ use crate::witness::PartialWitness;
 impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     /// Split the given element into a list of 11 targets, where each one represents a
     /// base-64 limb of the element, with little-endian ordering.
-    pub(crate) fn split_le_base64(&mut self, x: Target) -> Vec<Target> {
-        let gate = self.add_gate(BaseSumGate::<64>::new(11), vec![]);
+    pub(crate) fn split_le_base<const B: usize>(&mut self, x: Target) -> Vec<Target> {
+        let num_limbs = num_limbs_to_check(64, B);
+        let gate = self.add_gate(BaseSumGate::<B>::new(num_limbs), vec![]);
         let sum = Target::Wire(Wire {
             gate,
-            input: BaseSumGate::<64>::WIRE_SUM,
+            input: BaseSumGate::<B>::WIRE_SUM,
         });
         self.route(x, sum);
-        (BaseSumGate::<64>::WIRE_LIMBS_START..BaseSumGate::<64>::WIRE_LIMBS_START + 11)
+        (BaseSumGate::<B>::WIRE_LIMBS_START..BaseSumGate::<B>::WIRE_LIMBS_START + num_limbs)
             .map(|i| Target::Wire(Wire { gate, input: i }))
             .collect()
     }
 
     /// Asserts that `x`'s bit representation has at least `trailing_zeros` trailing zeros.
-    pub(crate) fn assert_trailing_zeros(&mut self, x: Target, trailing_zeros: u32) {
-        let limbs = self.split_le_base64(x);
-        for i in 0..ceil_div_usize(trailing_zeros as usize, 6) {
+    pub(crate) fn assert_trailing_zeros<const B: usize>(&mut self, x: Target, trailing_zeros: u32) {
+        let limbs = self.split_le_base::<B>(x);
+        let num_limbs_to_check = num_limbs_to_check(trailing_zeros, B);
+        assert!(
+            num_limbs_to_check < self.config.num_routed_wires,
+            "Not enough routed wires."
+        );
+        for i in 0..num_limbs_to_check {
             self.assert_zero(limbs[i]);
         }
     }
 }
+
+/// Returns `k` such that any number with `k` trailing zeros in base `base` has at least
+/// `n` trailing zeros in base 2.
+fn num_limbs_to_check(n: u32, base: usize) -> usize {
+    (n as f64 * (2.0_f64.log(base as f64))).ceil() as usize
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::circuit_data::CircuitConfig;
+    use crate::field::crandall_field::CrandallField;
+    use crate::fri::FriConfig;
+    use crate::prover::PLONK_BLINDING;
+    use crate::verifier::verify;
+    use anyhow::Result;
+
+    #[test]
+    fn test_split_base() -> Result<()> {
+        type F = CrandallField;
+        let config = CircuitConfig {
+            num_wires: 134,
+            num_routed_wires: 12,
+            security_bits: 128,
+            rate_bits: 3,
+            num_challenges: 3,
+            fri_config: FriConfig {
+                proof_of_work_bits: 1,
+                rate_bits: 3,
+                reduction_arity_bits: vec![1],
+                num_query_rounds: 1,
+                blinding: PLONK_BLINDING.to_vec(),
+            },
+        };
+        let mut builder = CircuitBuilder::<F, 4>::new(config);
+        let x = F::from_canonical_usize(0b10100000); // 160 =1120 in base 5.
+        let xt = builder.constant(x);
+        let limbs = builder.split_le_base::<5>(xt);
+        assert_eq!(limbs.len(), 28); // 5^27 < 2^64 <= 5^28
+        let zero = builder.zero();
+        let one = builder.one();
+        let two = builder.two();
+        builder.assert_equal(limbs[0], zero);
+        builder.assert_equal(limbs[1], two);
+        builder.assert_equal(limbs[2], one);
+        builder.assert_equal(limbs[3], one);
+
+        builder.assert_trailing_zeros::<3>(xt, 4);
+        builder.assert_trailing_zeros::<3>(xt, 5);
+        builder.assert_trailing_zeros::<13>(xt, 5);
+        let data = builder.build();
+
+        let proof = data.prove(PartialWitness::new());
+        verify(proof, &data.verifier_only, &data.common)
+    }
+}
diff --git a/src/gates/base_sum.rs b/src/gates/base_sum.rs
index 9190e19c..8c8064a1 100644
--- a/src/gates/base_sum.rs
+++ b/src/gates/base_sum.rs
@@ -102,7 +102,7 @@ impl<F: Extendable<D>, const D: usize, const B: usize> Gate<F, D> for BaseSumGat
     }
 
     fn num_constraints(&self) -> usize {
-        1 + B
+        1 + self.num_limbs
     }
 }