How Do I Choose the Best Digital Calculator?

Modern electronic calculators are hand-held electronic machines that can perform mathematical operations. They have integrated circuit chips, but the structure is much simpler than computers. It can be said to be the first generation of electronic computers (computers), and the functions are weak, but it is more convenient and It is cheap and can be widely used in commercial transactions. It is an essential office supply.

With STC89C52 single-chip microcomputer as the core, 4 × 4 matrix keyboard is used to input numbers, which can realize the operations of addition, subtraction, multiplication, and division, and then display the input process and calculation results on LCD12864, and the buzzer alarms. This system has the advantages of simple circuit structure, low development cost and convenient operation. ^[1]

Introduced the concept of significant digits and its calculation rules, introduced the general characteristics of calculators and their use skills, and gave calculation examples. ^[2]

Digital calculator calculator

Calculators are widely used electronic devices, most of which are 8-bit and 10-bit (for example, CA SIO's fx -80, fx -82 and fx -100D, etc., the first two are 8-bit and the latter are 10) Digits). This calculator can multiply, divide, add and subtract multiple values with 8 or 10 significant digits to get an answer with 8 or 10 significant digits.

So, will calculator calculations, especially the continuous calculation of a large amount of data, also produce the error of the last one or even the first two of the answers? In fact, calculator manufacturers have noticed this. At that time, The 10-digit calculator is `` 10-digit input, 12-digit operation inside the machine, and 10-digit display ''. The same is true for 8-bit calculators, which are 10-bit operations inside the machine. When the 12-bit or 10-bit operation is completed, the last two digits are cut off (rounded) and only the first 10 or 8 digits are displayed to avoid this disadvantage. Of course, if this kind of calculator can input 12 digits, it is even better.

Due to the advancement of chip technology, calculators on the market are all `` 10-bit input, 15-bit operation in the machine, 10-bit display '' (such as CASIO's fx -500ES, and even student-type fx -82ES). Many models can also allow 15-bit input, which can improve the calculation accuracy even more. ^[2]

Digital calculator familiar with calculator

Suppose you have a calculator that displays 10 digits. How do I know how many digits are calculated in the machine? For example, you can first calculate the square of 2 and press the 2 key and the square key. The display must be 1.414 213 562. Subtract an exact number 1.414 213 562 000 from here, which must be entered manually. If your machine performs 12-bit operations, the result of the 2 typed in the former is 1.414 213 562 37. Subtract the two to get 3.7 × 10 ^-10 . If the machine performs 15-bit operations, 2 is The calculation result in the machine is 1.414 213 562 373 09, which is subtracted from the manual input accurate value, which should be 3.7309 × 10 ^-10 . In this way, you can know the number of digits calculated in your calculator.

With this method, any 15-digit data in the machine can be retrieved. For example, the square of 1.234 567 891 is calculated and displayed as 1.524 157 877. The first 5 digits of 1.524 1 are subtracted from this to get 5.787 748 818 × 10 ^-5 . So, the 15-digit answer to get this square is 1.524 157 877 488 18. Under normal circumstances, only the last bit of the 15-bit data in the aircraft is unreliable. The result of the first 15 digits in the root number 2 machine is 1.414 213 562 373 09. Only the last digit 9 differs from the exact value by 1, because the root number 2 = 1.414 213 562 373 095 048 8 ... The 16th digit cut out is 5, which should be `` five in ''. Looking at the pi, the 15-digit display in the machine is 3.141 592 653 589 80, and the last digit is also different by 1 because = 3.141 592 653 589 793 238 ..., the 16th digit should be rounded off.

It can be seen that if this calculator can input 15 digits, it can be used as a 15-digit calculator. In fact, no matter how scientific research or teaching, ordinary physical calculations do not require such high accuracy. Even in the financial world, the amount in "yuan" has been accurate to the sixth decimal place. In addition to the calculator in your hand, you also have a super-high-precision calculator! Its name is ultra-high-precision, with 64-bit calculations and 32-bit display in the machine! This calculator is hidden in the computer.

Turn on the computer and find the calculator in the computer through [Start All Programs Accessories Calculator]. There are two, one is four calculators, and the other is a function calculator. The value of the Pi in the machine. Click on the pi ratio to display the 32-bit value, and then recall the last 32 digits in the machine. The in-machine calculation result of the pi is:

= 3.141 592 653 589 793 238 462 643 383 279 5 | 02884 197 169 399 3 | 11 481 966 593 000 570

In the value to the right of the equal sign, there are two vertical lines. The first vertical line is after the 32nd bit, which indicates the first 32 bits of the normal display. The second vertical line is after the 47th bit, which indicates the pi given in the machine The value is correct before 47 digits, and the vertical bar is wrong afterwards. That is to say, the 64-bit value obtained by the in-machine operation cannot be trusted with 17 digits.

First, it is clear that the value of the pi is calculated temporarily by a pre-stored formula program in the machine. The machine needs to calculate one by one, each item must be 64 bits, and then add up one by one, and it needs to add many many items to get accurate results. Even so, the last 17 digits in the result are Unreliable. It can be seen that the design selects "64-bit operation in the machine", and it makes sense to select so many bits. This can fully guarantee the correctness of the displayed value. ^[2]