diff --git a/src/main/scala/chisel3/util/BitPat.scala b/src/main/scala/chisel3/util/BitPat.scala
index 2cf8470605c..232b6da41a9 100644
--- a/src/main/scala/chisel3/util/BitPat.scala
+++ b/src/main/scala/chisel3/util/BitPat.scala
@@ -120,8 +120,7 @@ object BitPat {
   * }}}
   */
 sealed class BitPat(val value: BigInt, val mask: BigInt, w: Int) extends BitSet with SourceInfoDoc {
-  val onSet = value & mask
-  val offSet = ~value & mask
+  override val terms = Set(this)
   override lazy val width = w
 
   def getWidth: Int = w
@@ -158,14 +157,63 @@ sealed class BitPat(val value: BigInt, val mask: BigInt, w: Int) extends BitSet
     new BitPat((value << that.getWidth) + that.value, (mask << that.getWidth) + that.mask, this.width + that.getWidth)
   }
 
-  /** Generate raw string of a BitPat. */
-  def rawString: String = Seq.tabulate(width) { i =>
+  def overlap(rhs: BitPat): Boolean = ((mask & rhs.mask) & (value ^ rhs.value)) == 0
+
+  def cover(that: BitPat): Boolean = (mask & (~that.mask | (value ^ that.value))) == 0
+
+  def intersect(that: BitPat): BitSet = {
+    if (!overlap(that)) {
+      BitSet.emptyBitSet
+    } else {
+      new BitPat(this.value | that.value, this.mask | that.mask, this.width.max(that.width))
+    }
+  }
+
+  def subtract(that: BitPat): BitSet = {
+    require(width == that.width)
+    def enumerateBits(mask: BigInt): Seq[BigInt] = {
+      if (mask == 0) {
+        Nil
+      } else {
+        // bits comes after the first '1' in a number are inverted in its two's complement.
+        // therefore bit is always the first '1' in x (counting from least significant bit).
+        val bit = mask & (-mask)
+        bit +: enumerateBits(mask & ~bit)
+      }
+    }
+
+    val intersection = intersect(that)
+    val omask = this.mask
+    if (intersection.isEmpty) {
+      this
+    } else {
+      new BitSet {
+        val terms =
+          intersection.terms.flatMap { remove =>
+            enumerateBits(~omask & remove.mask).map { bit =>
+              // Only care about higher than current bit in remove
+              val nmask = (omask | ~(bit - 1)) & remove.mask
+              val nvalue = (remove.value ^ bit) & nmask
+              val nwidth = remove.width
+              new BitPat(nvalue, nmask, nwidth)
+            }
+          }
+      }
+    }
+  }
+
+  override def isEmpty: Boolean = false
+
+  /** Generate raw string of a BitSat. */
+  def rawString: String = Seq
+    .tabulate(width) { i =>
       (value.testBit(width - i - 1), mask.testBit(width - i - 1)) match {
-      case (true, true) => "1"
-      case (false, true) => "0"
-      case (_, false) => "?"
+        case (true, true)  => "1"
+        case (false, true) => "0"
+        case (_, false)    => "?"
+      }
     }
-  }.mkString
+    .mkString
 
   override def toString = s"BitPat($rawString)"
 }
diff --git a/src/main/scala/chisel3/util/BitSet.scala b/src/main/scala/chisel3/util/BitSet.scala
index 26ba20322c5..3fc0ef1bf26 100644
--- a/src/main/scala/chisel3/util/BitSet.scala
+++ b/src/main/scala/chisel3/util/BitSet.scala
@@ -2,112 +2,108 @@
 
 package chisel3.util
 
-trait BitSetFamily { bsf =>
-  val terms: Set[BitSet]
-
-  // set width = 0 if terms is empty.
+trait BitSet { bsf =>
+  val terms: Set[BitPat]
+
+  /**
+    * Get specified width of said BitSetFamily
+    *
+    * All BitPat contained in one family should have the same width
+    */
   lazy val width: Int = {
-    assert(terms.map(_.width).size < 1)
+    assert(terms.map(_.width).size <= 1)
+    // set width = 0 if terms is empty.
     terms.headOption.map(_.width).getOrElse(0)
   }
 
-  override def toString: String = terms.toSeq.sortBy((t: BitSet) => (t.onSet, t.offSet)).mkString("\n")
+  override def toString: String = terms.toSeq.sortBy((t: BitPat) => (t.mask, t.value)).mkString("\n")
 
+  /**
+    * @return whether the BitSetFamily is empty (i.e. no value matches)
+    */
   def isEmpty: Boolean = terms.forall(_.isEmpty)
 
-  def cover(that: BitSetFamily): Boolean =
-    if (terms.isEmpty)
-      that.terms.isEmpty
-    else
-      terms.flatMap(a => that.terms.map(b => (a, b))).foldLeft(true) {
-        case (left, (a, b)) => a.cover(b) & left
-      }
-
-  def intersect(that: BitSetFamily): BitSetFamily = new BitSetFamily {
-    val terms = bsf.terms.flatMap(a => that.terms.map(b => a.intersect(b))).filterNot(_.isEmpty)
+  /**
+    * @return whether this BitSetFamily overlap with that BitSetFamily, i.e. !(intersect.isEmpty)
+    */
+  def overlap(that: BitSet): Boolean = {
+    !bsf.terms.flatMap(a => that.terms.map(b => (a, b))).forall { case (a, b) => !a.overlap(b) }
   }
 
-  def subtract(that: BitSetFamily): BitSetFamily = new BitSetFamily {
-    val terms = bsf.terms.flatMap(a => that.terms.map(b => a.subtract(b))).filterNot(_.isEmpty)
-  }
-
-  def union(that: BitSetFamily): BitSetFamily = new BitSetFamily {
+  /**
+    * @param that BitSetFamily to be covered
+    * @return whether this BitSetFamily covers that (i.e. forall b matches that, b also matches this)
+    */
+  def cover(that: BitSet): Boolean =
+    that.subtract(this).isEmpty
+
+  /**
+    * @return a BitSetFamily that only match a value when both operand match
+    */
+  def intersect(that: BitSet): BitSet =
+    bsf.terms
+      .flatMap(a => that.terms.map(b => a.intersect(b)))
+      .filterNot(_.isEmpty)
+      .fold(BitSet.emptyBitSet)(_.union(_))
+
+  /**
+    * Subtract that from this BitSetFamily
+    * @param that subtrahend
+    */
+  def subtract(that: BitSet): BitSet =
+    bsf.terms.map { a =>
+      that.terms.map(b => a.subtract(b)).fold(a)(_.intersect(_))
+    }.filterNot(_.isEmpty).fold(BitSet.emptyBitSet)(_.union(_))
+
+  /**
+    * Union of two BitSetFamily
+    */
+  def union(that: BitSet): BitSet = new BitSet {
     val terms = bsf.terms ++ that.terms
   }
 
+  /**
+    * Test whether two BitSetFamily matches the same set of value
+    *
+    * Caution: This method can be very expensive compared to ordinary == operator between two Objects
+    */
   override def equals(obj: Any): Boolean = {
     obj match {
-      case that: BitSetFamily => if (width == that.width) this.cover(that) && that.cover(this) else false
+      case that: BitSet => if (width == that.width) this.cover(that) && that.cover(this) else false
       case _ => false
     }
   }
 }
 
-trait BitSet extends BitSetFamily { b =>
-  override val terms = Set(this)
-  val onSet:  BigInt
-  val offSet: BigInt
-  val width:  Int
-
-  assert(width > 0)
-
-  def cover(that: BitSet) = ((onSet & that.onSet) == that.onSet) & ((offSet & that.offSet) == that.offSet)
-
-  def intersect(that: BitSet): BitSet = {
-    require(width == that.width)
-    new BitSet {
-      val onSet:               BigInt = b.onSet & that.onSet
-      val offSet:              BigInt = b.offSet & that.offSet
-      override lazy val width: Int = b.width
-    }
+object BitSet {
+  val emptyBitSet: BitSet = new BitSet {
+    override val terms = Set()
   }
 
-  def subtract(that: BitSet): BitSet = {
-    require(width == that.width)
+  def apply(str: String): BitSet = {
     new BitSet {
-      val onSet:               BigInt = b.onSet & ~that.onSet
-      val offSet:              BigInt = b.offSet & ~that.offSet
-      override lazy val width: Int = b.width
-    }
-  }
-
-  override def isEmpty: Boolean = (onSet | offSet) == 0
-  override def toString: String = Seq
-    .tabulate(width) { i =>
-      (onSet.testBit(i), offSet.testBit(i)) match {
-        case (true, true)   => "-"
-        case (true, false)  => "1"
-        case (false, true)  => "0"
-        case (false, false) => "~"
-      }
-    }
-    .mkString
-}
-
-object BitSet {
-  def apply(str: String): BitSetFamily = {
-    new BitSetFamily {
       val terms = str
         .split('\n')
-        .map(str =>
-          new BitSet {
-            val onSet: BigInt = str.zipWithIndex.map {
-              case ('-' | '1', i) => BigInt(1) << i
-              case ('~' | '0', _) => BigInt(0)
-              case _              => throw new Exception("bitset parse error")
-            }.sum
-            val offSet: BigInt = str.zipWithIndex.map {
-              case ('-' | '0', i) => BigInt(1) << i
-              case ('~' | '1', _) => BigInt(0)
-              case _              => throw new Exception("bitset parse error")
-            }.sum
-            override lazy val width: Int = str.length
-          }
-        ).toSet
+        .map(str => BitPat(str))
+        .toSet
+      assert(terms.map(_.width).size <= 1)
     }
   }
 
-  def decode(input: chisel3.UInt, bitSets: Seq[BitSetFamily], errorBit: Boolean = false) =
+  /**
+    * Generate a decoder circuit that matches the input to each bitSet.
+    *
+    * The resulting circuit functions like the following but is optimized with a logic minifier
+    * when(input === bitSets(0)) { output := b000001 }
+    * .elsewhen (input === bitSets(1)) { output := b000010 }
+    * ....
+    * .otherwise { if (errorBit) output := b100000 else output := DontCare }
+    *
+    * @param input input to the decoder circuit, width should be equal to bitSets.width
+    * @param bitSets set of ports to be matched, all width should be the equal
+    * @param errorBit whether generate an additional decode error bit
+    */
+  def decode(input: chisel3.UInt, bitSets: Seq[BitSet], errorBit: Boolean = false): chisel3.UInt =
     chisel3.util.experimental.decode.decoder(
       input,
       chisel3.util.experimental.decode.TruthTable(
diff --git a/src/test/scala/chiselTests/util/BitPatSpec.scala b/src/test/scala/chiselTests/util/BitPatSpec.scala
index 0c83493fe35..78d1ad75a0e 100644
--- a/src/test/scala/chiselTests/util/BitPatSpec.scala
+++ b/src/test/scala/chiselTests/util/BitPatSpec.scala
@@ -24,7 +24,7 @@ class BitPatSpec extends AnyFlatSpec with Matchers {
     intercept[IllegalArgumentException]{BitPat("b")}
   }
 
-  it should "contact BitPat via ##" in {
+  it should "concat BitPat via ##" in {
     (BitPat.Y(4) ## BitPat.dontCare(3) ## BitPat.N(2)).toString should be (s"BitPat(1111???00)")
   }
 
diff --git a/src/test/scala/chiselTests/util/BitSetSpec.scala b/src/test/scala/chiselTests/util/BitSetSpec.scala
new file mode 100644
index 00000000000..730182cf013
--- /dev/null
+++ b/src/test/scala/chiselTests/util/BitSetSpec.scala
@@ -0,0 +1,94 @@
+package chiselTests.util
+
+import chisel3.util.{BitPat, BitSet}
+import org.scalatest.flatspec.AnyFlatSpec
+import org.scalatest.matchers.should.Matchers
+
+class BitSetSpec extends AnyFlatSpec with Matchers {
+  behavior of classOf[BitSet].toString
+
+  it should "reject unequal width when constructing a BitSet" in {
+    intercept[AssertionError] {
+      BitSet(
+        """b0010
+          |b00010
+          |""".stripMargin)
+    }
+  }
+
+  it should "return empty subtraction result correctly" in {
+    val aBitPat = BitPat("b10?")
+    val bBitPat = BitPat("b1??")
+
+    aBitPat.subtract(bBitPat).isEmpty should be (true)
+  }
+
+  it should "return nonempty subtraction result correctly" in {
+    val aBitPat = BitPat("b10?")
+    val bBitPat = BitPat("b1??")
+    val cBitPat = BitPat("b11?")
+    val dBitPat = BitPat("b100")
+
+    val diffBitPat = bBitPat.subtract(aBitPat)
+    bBitPat.cover(diffBitPat) should be (true)
+    diffBitPat.equals(cBitPat) should be (true)
+
+    val largerdiffBitPat = bBitPat.subtract(dBitPat)
+    aBitPat.cover(dBitPat) should be (true)
+    largerdiffBitPat.cover(diffBitPat) should be (true)
+  }
+
+  it should "be able to handle complex subtract between BitSet" in {
+    val aBitSet = BitSet(
+      """b?01?0
+        |b11111
+        |b00000
+        |""".stripMargin)
+    val bBitSet = BitSet(
+      """b?1111
+        |b?0000
+        |""".stripMargin
+    )
+    val expected = BitPat("b?01?0")
+
+    expected.equals(aBitSet.subtract(bBitSet)) should be (true)
+  }
+
+  it should "be generated from BitPat union" in {
+    val aBitSet = BitSet(
+      """b001?0
+        |b000??""".stripMargin)
+    val aBitPat = BitPat("b000??")
+    val bBitPat = BitPat("b001?0")
+    val cBitPat = BitPat("b00000")
+    aBitPat.cover(cBitPat) should be (true)
+    aBitSet.cover(bBitPat) should be (true)
+
+    aBitSet.equals(aBitPat.union(bBitPat)) should be (true)
+  }
+
+  it should "be generated from BitPat substraction" in {
+    val aBitSet = BitSet(
+      """b001?0
+        |b000??""".stripMargin)
+    val aBitPat = BitPat("b00???")
+    val bBitPat = BitPat("b001?1")
+
+    aBitSet.equals(aBitPat.subtract(bBitPat)) should be (true)
+  }
+
+  it should "union two BitSet together" in {
+    val aBitSet = BitSet(
+      """b001?0
+        |b001?1
+        |""".stripMargin)
+    val bBitSet = BitSet(
+      """b000??
+        |b01???
+        |""".stripMargin
+    )
+    val cBitPat = BitPat("b0????")
+    cBitPat.equals(aBitSet.union(bBitSet)) should be (true)
+  }
+
+}