I am trying to convert some binary data to decimal numbers. I succeeded to convert binary to hex, but now I want to do the same with binary to decimal. I want to use bitwise operators and NO array.

See my code from binairy to hex. The incoming data is 8 bits. This code first calculates the most significant number, and then, the least significant number. This works good, but I cannot figure it out for bin to dec

The function console_print_char is sort of the printf function of my program.

    void console_print_hex_char(unsigned char data){
    unsigned char temp;

        temp = (data >> 4);
            if(temp> 9) console_print_char(temp + ('A'- 10));
            else console_print_char(temp + '0');
        temp = data & 0x0F;
        if(temp> 9) console_print_char(temp + ('A'- 10));
        else console_print_char(temp + '0');
  • 2
    your question is a general programming question that is not related to the Arduino ... please delete your post and go here stackoverflow.com/questions
    – jsotola
    Mar 17, 2020 at 17:22
  • note: you have a stray }, that is outside of the "code area" of your post
    – jsotola
    Mar 17, 2020 at 17:25
  • @jsotola is right, you might need to push this over to SO. Anyway, the conversion of a binary number into decimal is most simply done with modulo (%) and divide (/) if you don't want to use library functions. Additionally, there is an algorithm that involves shifting bit by bit, and some conditional adding of 3. Unfortunately I don't have an URL at hand. Mar 17, 2020 at 21:07
  • 1
    Binary is spelled B-I-N-A-R-Y. It's bi-na-ry, not bin-air-y.
    – Duncan C
    Mar 17, 2020 at 22:07
  • You can google Binary to BCD conversion. There are pretty short algorithms that do this. After the conversion each decimal digit is stored in a nibble.
    – Kwasmich
    Mar 19, 2020 at 16:20

2 Answers 2


You cannot do what you are trying to do. There is no direct correspondence between some number of bits and a decimal digit.

With hexadecimal, every 4 bits corresponds to exactly 1 hex digit. That is why hex is used for computers.

One hex digit represents exactly 4 bits. Every time you add another hex digit, you add 4 bits.

Two hex digits corresponds to exactly a byte. 00h to FFh represents a value from 0 to 255.

There is no such direct correspondence between binary and decimal. If you have 4 bits, it takes 1 or 2 decimal digits to represent it (0-15) If you have 8 bits, it takes 1, 2, or 3 decimal digits to represent it, but there are 3 digit decimal values (values > 255) that you can't represent with 8 bits.

Binary  Hex Decimal
0000    0   0
0001    1   1
0010    2   2
0011    3   3
0100    4   4
0101    5   5
0110    6   6
0111    7   7
1000    8   8
1001    9   9
1010    A   10
1011    B   11
1100    C   12
1101    D   13
1110    E   14
1111    F   15

You simply cannot convert a binary number to decimal using bit shifting and masking.

As @Kwasmich says in their answer, the closest you're likely to come would be to convert your binary value to BCD (Binary coded decimal) where each 4 bits holds a decimal digit. You could convert THAT to decimal character output using masking and shifting.


here's the c++ code

    vector<int> b={1,0,1,0,1,0,1};
        int sum=0;
        for(int i=b.size()-1, j=0; i>=0; i--, j++){
        return sum;
  • That is a way to convert a series of bits to decimal. Note the it uses multiplication and arrays, both of which the OP wants to avoid.
    – Duncan C
    Jun 27, 2020 at 1:43
  • 1
    BTW, it's silly to use b[j] * (1<<i). That's an unneeded multiplication. Just use sum += b[j]<<i` If b[j] is 0, it shifts nothing for that bit. If b[j] is a 1 bit, it shifts a one to the appropriate magnitude, without the need of a multiply.
    – Duncan C
    Jun 27, 2020 at 1:46

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