Both buttons are used to clear or cancel an entry. The C button will clear all input to the calculator while the CE button clears the most recent entry ONLY. It means if you have made a mistake in a long computation you can just press CE and don’t need to start all over again.
According to Vintage Calculators, this feature has been incorporated in calculators from early models. The first electronic calculator released by Bell Punch Co., Uxbridge, England in 1961 were the Anita Mk VII and the Anita Mk 8.
Anita Mk8 had a Clear Register and Clear Keyboard button which continued in later models such as Sanyo ICC-0081 which had CK (Clear Keyboard) and CA (Clear All) button. There was also version of calculators with C (Clear) and CI (Cancel Input) button.
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