Unable to convert true/false to 1/0 using xsl:when

I am trying to use XSL to convert XML attributes from having values of "true"/"false" to values of "1"/"0", but I am unable to make the conversion. From reading online, I should be able to use either <xsl:when> or <xsl:if> to accomplish this. Some references wrap my attribute in string, some do not.

Take the example XML:

<root>
  <record name="a" isMutable="true">
  <record name="b" isMutable="false">
</root>

And the example XSL:

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet>
  <xsl:template match="root">
    <top>
      <xsl:apply-templates select="/root/record"/>
    </top>
  </xsl:template>
  <xsl:template match="/root/record">
    <xsl:element name="element">
      <xsl:choose>
        <xsl:when test="string(@isMutable) = 'true'">
          <xsl:attribute name="when_value">1</xsl:attribute>
        </xsl:when>
        <xsl:when test="string(@isMutable) = 'false'">
          <xsl:attribute name="when_value">0</xsl:attribute>
        </xsl:when>
        <xsl:otherwise>
          <xsl:attribute name="plain_value"><xsl:value-of select="@isMutable"/></xsl:attribute>
          <xsl:attribute name="bool_value"><xsl:value-of select="boolean(@isMutable = 'true')"/></xsl:attribute>
        </xsl:otherwise>
      </xsl:choose>
    </xsl:element>
  </xsl:template>
</xsl:stylesheet>

My hope is to get attributes with when_value="0" and when_value="1", instead I get:

<top>
  <element plain_value="true" bool_value=""/>
  <element plain_value="false" bool_value=""/>
</top>

I can see in the plain_value attribute that my attribute value is getting picked up. I also tried an alternate solution which tries to use boolean, but you can see that this produces a blank result. Can anyone please point out my syntax error(s) in my example XSL code? Thank you.