Re: Can you tell me how a calculator calculate ( works)

Wow, Vincent. The bigger question is, how can we explain how a calculator works, to your 5 year old son? First, my hats off to your son - it's great that he is interested in how things work at such a young age.

Here is the best I can do to explain things at what I hope is a level your son can understand:

Luckily, calculators can use arithmetic that is easy compared to the arithmetic you will be learning or have been learning.

You learn adding by memorized addition facts like:

4 + 3 = 7
and
2 + 9 = 11
and
5 + 5 = 10
and 
8 + 7 = 15

Our arithmetic system is based on the number 10. When you say 34, thirty four, you mean 3 tens and 4 ones. We use this ten-based system because we have 10 fingers and 10 toes, so we based oour system on counting with our fingers and toes..which is how we kind of started off. We can represent 10 numbers with our 10 fingers.

Luckily, as I said before - the calculator uses arithmetic that is a bit easier. A calculator has no fingers or toes...but it can change voltage levels, like the voltage on the batteries you use in your flashlights and in some of your toys. You can connect the battery, and turn the flashlight or toy "ON" or "OFF". These two levels, ON or OFF, are the two levels that the calculator uses in its arithmetic.

Let's call the "OFF" level "0", and the "ON" level "1". In this simpler arithmetic system, instead of 100 addition facts, there are only 4:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = two... which in this type of arithmetic is written as:
1 + 1 = 10 (because there is no 2 in a system with just 1's and 0's)

So, the calculator only has to deal with 4 addition facts.

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10

hundreds     tens    ones
      4         7       3         = 4 hundreds + 7 tens + 3 ones = 473

eights fours  twos   ones
  1        1     0      1         = 1 eights + 1 fours + 1 ones = 13 (thirteen)
and
  0        1     1      1         = 1 fours + 1 twos + 1 ones = 7 (seven)
and
  0        1     0      0         = 1 fours = 4 (four) 
and
  1        0     0      1         = 1 eights + 1 ones = 9 (nine)

Step 1) Convert the first number to be added from decimal to binary

9 in decimal is 1 0 0 1 in binary.... (see above.. 1 in the eights column plus 1 in the one's column = 9)

Step 2) Put it in a memory storage place (called a register) to use later

Step 3) Convert the second number to be added from decimal to binary

4 in decimal is 0 1 0 0 in binary (see above... 1 in the fours column is 4)

Step 4) Put it in another register

Step 5) Add the two numbers in the registers using binary addition

       1 0 0 1
    +  0 1 0 0
    -----------
    =  1 1 0 1 in binary  (try it yourself)
    

Step 6) Convert the number from binary to decimal

From above, you can see that 1 1 0 1 in binary is 1 eights plus 1 fours plus 0 twos plus 1 ones = 8 + 4 + 1 = 13.

I don't know if this is way too complicated for your son...it may be..but it's as simple as I can make these complex concepts.