Where can I find information about this, what queries to enter in Google?

Question

Computers

1) Does the base of integer (fractional) numbers determine the accuracy of calculations? How can the base (as I understand it, the number system) affect the accuracy of calculations, different methods of converting from one number system to another? Didn't they learn how to convert numbers with infinite precision a long time ago?
2) If we add two binary 8-bit values ​​of signed integers 1110 1001 and 1100 0010 as a result we get overflow?
What is the difference between unsigned addition of the same binary numbers?
3) Do I need to use special fractional commands to add data encoded in IEEE754 format? (there are such?, maybe I translated it wrong)

Answer 1

1) Does the base of integer (fractional) numbers determine the accuracy of calculations?

integers - no, floating point - maybe.

How can the base (as I understand it, the number system) affect the accuracy of calculations

choosing a base for the floating point format is roughly equivalent to changing the number of bits for the mantissa and exponent. The larger the base, the less information about the mantissa and the greater the range of possible values. Accordingly, the accuracy drops.

different methods of converting from one number system to another

the number system of any number only affects the final form of the number on the screen

Didn't they learn how to convert numbers with infinite precision a long time ago?

Depending on what you mean. What if the number is irrational? how do you write the square root of 2 with infinite precision?

2) If we add two binary 8-bit values ​​of signed integers 1110 1001 and 1100 0010 as a result we get overflow?

yes, there will be an overflow of 8 bits, resulting in a positive number

What is the difference between unsigned addition of the same binary numbers?

in different commands to the processor and, accordingly, different results in some cases

3) Do I need to use special fractional commands to add data encoded in IEEE754 format? (there are such?, maybe I translated it wrong)

well, yes, modern processors have a module for floating point calculations, there is a separate set of instructions. if it's a CPU with no support for fractional calculations, everything is computed in software.