diff --git a/src/kyupy/logic.py b/src/kyupy/logic.py
index 14a3e83..3e97f8e 100644
--- a/src/kyupy/logic.py
+++ b/src/kyupy/logic.py
@@ -269,6 +269,18 @@ def mv_to_bp(mva):
     return np.packbits(unpackbits(mva)[...,:3], axis=-2, bitorder='little').swapaxes(-1,-2)
 
 
+def mv_init(mva):
+    """Returns the initial binary values for mva.
+    """
+    return (mva>>1) & ((mva>>2)|mva) & 1
+
+
+def mv_final(mva):
+    """Returns the final binary value of mva.
+    """
+    return mva & ((mva>>2)|(mva>>1)) & 1
+
+
 def bparray(*a):
     """Converts (lists of) Boolean values or strings into a bit-parallel array.
 
diff --git a/src/kyupy/logic_sim.py b/src/kyupy/logic_sim.py
index 26a1c76..0aca25c 100644
--- a/src/kyupy/logic_sim.py
+++ b/src/kyupy/logic_sim.py
@@ -10,7 +10,7 @@ import math
 
 import numpy as np
 
-from . import numba, logic, hr_bytes, sim, eng
+from . import numba, logic, hr_bytes, sim, eng, cdiv
 from .circuit import Circuit
 
 class LogicSim(sim.SimOps):
@@ -28,7 +28,7 @@ class LogicSim(sim.SimOps):
         self.m = m
         self.mdim = math.ceil(math.log2(m))
         self.sims = sims
-        nbytes = (sims - 1) // 8 + 1
+        nbytes = cdiv(sims, 8)
 
         self.c = np.zeros((self.c_len, self.mdim, nbytes), dtype=np.uint8)
         self.s = np.zeros((2, self.s_len, 3, nbytes), dtype=np.uint8)