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Autonomous robotic navigation and mapping have been of tremendous interest during the last decade. While several approaches have been presented, little is known about performing these tasks when constraints are placed on the processing resources and sensors. This paper studies the effectiveness in performing a few high level tasks when a mobile robot is equipped merely with a low-end microcontroller and four ultrasonic sensors. It is shown that the data memory on the microcontroller plays a crucial role in map construction of indoor environment. Four sensors are shown to be adequate for good quality map construction and for following a wall reasonably well. Experiments on map construction and wall following in an indoor environment using a mobile robot equipped with merely an Atmel 89C52 (and no external memory) are presented.