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This paper presents a set of comprehensive techniques for the intratask voltage-scheduling problem to reduce energy consumption in hard real-time tasks of embedded systems. Based on the execution profile of the task, a voltage-scheduling technique that optimally determines the operating voltages to individual basic blocks in the task is proposed. The obtained voltage schedule guarantees minimum average energy consumption. The proposed technique is then extended to solve practical issues regarding transition overheads, which are totally or partially ignored in the existing approaches. Finally, a technique involving a novel extension of our optimal scheduler is proposed to solve the scheduling problem in a discretely variable voltage environment. We also present a novel voltage set-up technique to determine each voltage level for customizable systems-on-chips (SoCs) with discretely variable voltages. In summary, it is confirmed from experiments that the proposed optimal scheduling technique reduces energy consumption by 20.2% over that of one of the state-of-the-art schedulers (Shin and Kim, 2001) and, further, the extended technique in a discrete-voltage environment reduces energy consumption by 45.3% on average.