How exactly does binary code get converted into letters?

Question

Out of curiosity, how exactly does binary code get converted into letters? I know there are sites that automatically convert binary to words for you but I wanna understand the specific, intermediary steps that binary code goes through before being converted into letters.

Answer 1

Here's a way to convert binary numbers to ASCII characters that is often simple enough to do in your head.

1 - Convert every 4 binary digits into one hex digit.

Here's a binary to hex conversion chart:

0001 = 1  0010 = 2  0011 = 3  0100 = 4  0101 = 5 0110 = 6 0111 = 7 1000 = 8  1001 = 9 1010 = a (the hex number a, not the letter a) 1011 = b 1100 = c 1101 = d 1110 = e 1111 = f 

(The hexadecimal numbers a through f are the decimal numbers 10 through 15. That's what hexadecimal, or "base 16" is - instead of each digit being capable of representing 10 different numbers [0 - 9], like decimal or "base 10" does, each digit is instead capable of representing 16 different numbers [0 - f].)

Once you know that chart, converting any string of binary digits into a string of hex digits is simple.

For example,

01000100 = 0100 0100 = 44 hex 1010001001110011 = 1010 0010 0111 0011 = a273 hex 

Simple enough, right? It is a simple matter to convert a binary number of any length into its hexadecimal equivalent.

(This works because hexadecimal is base 16 and binary is base 2 and 16 is the 4th power of 2, so it takes 4 binary digits to make 1 hex digit. 10, on the other hand, is not a power of 2, so we can't convert binary to decimal nearly as easily.)

2 - Split the string of hex digits into pairs.

When converting a number into ASCII, every 2 hex digits is a character. So break the hex string into sets of 2 digits.

You would split a hex number like 7340298b392 this into 6 pairs, like this:

7340298b392 = 07 34 02 98 b3 92 

(Notice I prepended a 0, since I had an odd number of hex digits.)

That's 6 pairs of hex digits, so its going to be 6 letters. (Except I know right away that 98, b3 and 92 aren't letters. I'll explain why in a minute.)

3 - Convert each pair of hex digits into a decimal number.

Do this by multiplying the (decimal equivalent of the) left digit by 16, and adding the 2nd.

For example, b3 hex = 11*16 + 3, which is 110 + 66 + 3, which is 179. (b hex is 11 decimal.)

4 - Convert the decimal numbers into ASCII characters.

Now, to get the ASCII letters for the decimal numbers, simply keep in mind that in ASCII, 65 is an uppercase 'A', and 97 is a lowercase 'a'.

So what letter is 68?

68 is the 4th letter of the alphabet in uppercase, right?
65 = A, 66 = B, 67 = C, 68 = D.

So 68 is 'D'.

You take the decimal number, subtract 64 for uppercase letters if the number is less than 97, or 96 for lowercase letters if the number is 97 or larger, and that's the number of the letter of the alphabet associated with that set of 2 hex digits.

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Alternatively, if you're not afraid of a little bit of easy hex arithmetic, you can skip step 3, and just go straight from hex to ASCII, by remembering, for example, that

hex 41 = 'A'  hex 61 = 'a' 

So subtract 40 hex for uppercase letters or 60 hex for lowercase letters, and convert what's left to decimal to get the alphabet letter number.

For example

01101100 = 6c, 6c - 60 = c = 12 decimal = 'l' 01010010 = 52, 52 - 40 = 12 hex = 18 decimal = 'R' 

(When doing this, it's helpful to remember that 'm' (or 'M') is the 13 letter of the alphabet. So you can count up or down from 13 to find a letter that's nearer to the middle than to either end.)

I saw this on a shirt once, and was able to read it in my head:

01000100 01000001 01000100 

I did it like this:

01000100 = 0100 0100 = 44 hex, - 40 hex = ucase letter 4 = D 01000001 = 0100 0001 = 41 hex, - 40 hex = ucase letter 1 = A 01000100 = 0100 0100 = 44 hex, - 40 hex = ucase letter 4 = D 

The shirt said "DAD", which I thought was kinda cool, since it was being purchased by a pregnant woman. Her husband must be a geek like me.

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How did I know right away that 92, b3, and 98 were not letters?

Because the ASCII code for a lowercase 'z' is 96 + 26 = 122, which in hex is 7a. 7a is the largest hex number for a letter. Anything larger than 7a is not a letter.

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So that's how you can do it as a human.

How do computer programs do it?

For each set of 8 binary digits, convert it to a number, and look it up in an ASCII table.

(That's one pretty obvious and straight forward way. A typical programmer could probably think of 10 or 15 other ways in the space of a few minutes. The details depend on the computer language environment.)