How do fission and fusion release energy?

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Mathstermind
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So we’ve just covered fission and fusion in class and I’m still at a loss as to how they release energy. I get that we go from a less stable nucleus to a more stable nucleus. But to work out the energy release we work out the mass change and use e=mc^2 . My issue is that, surely this mass change goes into the binding energy of the new nuclei (or nucleus) as the new nuclei or (nucleus) have a higher binding energy? If so then surely there’s no energy released bc that increased binding energy is ‘trapped’ in the new nuclei (or nucleus)??
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anosmianAcrimony
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The binding energy of a nucleus is the energy needed to break apart that nucleus. It isn't stored or trapped in the nucleus. A nucleus with a higher binding energy is more stable.
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