When any person has been convicted of a misdemeanor or of the violation of any ordinance of a municipal corporation, by any court or magistrate of the state, or of such municipal corporation, in a county or municipal corporation having no workhouse, and the commissioners of such county or council of such municipal corporation have made provisions as allowed by law for receiving persons so convicted into the workhouse of a city in any other county or district, or a joint city and county workhouse, or county workhouse in this state, it shall be competent for such court or magistrate, in its discretion, where imprisonment in the county or municipal jail may by law or ordinance be imposed in punishment of such offense, to sentence such person to such workhouse for a period not exceeding the maximum period of confinement in the county or municipal jail allowed by statute or ordinance for such offense; and in all such cases such court or magistrate may further order that such person stand committed to such workhouse until the costs of prosecution are paid, or he be discharged, as herein provided; and in all cases where a fine may be imposed in whole or in part punishment of an offense, or for violation of an ordinance of any municipal corporation, and such court or magistrate could order that such person stand committed to the jail of the county or municipal corporation until such fine and costs of prosecution are paid, such court or magistrate may order that such person stand committed to such workhouse until such fine and costs of prosecution are paid, or until he be discharged therefrom by allowing a credit of 60¢ per day on such fine and costs for each day of confinement in such workhouse, or be otherwise legally discharged.