CODEWITHSUNDEEP
binarydecimalcpu-architecture
beary605
beary605

Reputation: 824

Binary to Decimal in Computers

How does a computer turn binary, say, 110011 (51), to the corresponding ASCII values, 53('5') and 49('1')? Furthermore, how does a computer turn 53 and 49 back to 110011?

Upvotes: 2

Views: 2691

Answers (4)

James Youngman
James Youngman

Reputation: 3733

Binary to decimal conversion normally works as a repeated division loop. If we start with a number N, (N mod 10) is the final digit and then we proceed by dividing N by 10 and repeating to get the other digits.

  1. We start with N=51
  2. 51 mod 10 is 1. The final digit is 1.
  3. Divide by 10 to discard the digit we just extracted (integer division rounds), giving 5.
  4. (this is a repeat of step 2, with different N) 5 mod 10 is 5. The next digit is 5.
  5. 5/10 is 0 (rounding) and so we're done. The digits in reverse order are 1 and 5.
  6. We add 48 to each of the digit values to get the corresponding decimal digits in ASCII.
  7. So the end result is "51".

Converting from a string to the internal representation is even easier.

  1. Start with 0 in the accumulator
  2. Take the first character (here "5"). That's ASCII 53. Subtract 48 to get 5.
  3. Add that to our accumulator to get 0+5=5.
  4. Notice that there is another digit. Multiply the accumulator by 10 to get 50.
  5. Go back to step 1

In the next iteration (i.e. for "1"=ASCII 49) Subtract 48 again: 49-48=1. We add 1 to the accumulator giving 51. No more characters so we are done and the result is 51.

The fact that the computer's internal representation is binary is incidental. We only need to be able to add, subtract and multiply to convert a string to a number inside the computer.

(Of course subtraction is just addition of a negative number and multiplication is just a sequence of additions, so addition is all that's really needed.)

Upvotes: 4

David Buck
David Buck

Reputation: 2847

To turn binary into ASCII:

1) take your number divide it by 10 decimal (1010 binary) and calculate the remainder 2) With the remainder, add 48 (the ASCII value for '0'). This gives you the last digit. 3) If the quotient is 0, stop 4) If the quotient is more than 0, start again from step 1 using the quotient.

Eg. Convert 51 (110011) to ASCII using base 10 (1010):

110011 / 1010  = 0101 (5 decimal) remainder 0001


0001 (the remainder from above) + 110000 ('0') = 110001 (49 decimal or '1' in ASCII)

0101 (the quotient from above) / 1010 = 0 remainder 0101
0101 (the remainder) + 110000 ('0') = 110101 (53 decimal or '5' in ASCII)

Upvotes: 0

QuantumMechanic
QuantumMechanic

Reputation: 13946

It doesn't turn them either way. The 53 is always a 53 in memory.

What happens is that when it needs to be displayed, a function gets called that knows that when it sees the number 53, it generates the graphics our eyes see as a 5. Or within memory it may turn the number 53 into the numbers 53 and 51, which ultimately some program will display as the characters "5" and "3".

And the 53 is always 110101. A memory cell is a sequence of bits and holds decimal 53 as the bits 001101011.

Again, there are functions that see those bits and can generate on your screen the character "5" and the character "3".

But inside the computer its always numbers and its always binary.

Upvotes: 0

bmargulies
bmargulies

Reputation: 100040

Try to write a computer program for this purpose. It's generally done in software, though some processors have special purpose decimal instructions. Just pretend that it's your job to look at slips of paper with binary integers on them and produce slips of paper with Unicode code points on them, and you'll have the basic outline in no time.

Upvotes: 0

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