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(a) It shall be the duty of the justice of the peace or the clerk of the court rendering a judgment or sentence of conviction in misdemeanor cases when the defendant is committed to the county jail to file a copy of the judgment or sentence in the office of the clerk of the county court, together with a full itemized statement of the fine and costs adjudged, as well as a concise statement of the time the convict may be held to labor in discharge of the judgment or sentence.
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(b) The clerk of the county court shall register the judgment or sentence in a book to be kept by him or her for that purpose.
