C - fast conversion between binary and hexadecimal representations

Question

Reading or writing C code, I often have difficulty translating numbers from binary to hexadecimal and vice versa. Typically, various masks, such as 0xAAAA5555 , are very often used in low-level programming, but it is difficult to recognize the particular set of bits that they represent. Is there any catchy rule on how to do this quickly in the mind?

Answer 1

Each card with a hexadecimal digit is exactly 4 bits, I usually remember 8421 the weights of each of these bits, so it’s very easy to even make a conversion in mind, i.e.

A = 10 = 8 + 2 = 1010 ... 5 = 4 + 1 = 0101

just keep the scales 8-4-2-1 .

 A 5 8+4+2+1 8+4+2+1 1 0 1 0 0 1 0 1 

Answer 2

It is always easy for me to match HEX with binary numbers. Since each hexadecimal digit can be directly mapped to a four-digit binary number , you can think of:

 > 0xA4 

how

 > b 1010 0100 > ---- ---- (4 binary digits for each part) > A 4 

Answer 3

The conversion is calculated by dividing the base 10 representation by 2 and applying the remainder in the reverse order. I do it in my head, it seems to work.

So you say what 0xAAAA5555 looks 0xAAAA5555

I just understand how A looks and 5 looks by doing

 A = 10 10 / 2 = 5 r 0 5 / 2 = 2 r 1 2 / 2 = 1 r 0 1 / 2 = 0 r 1 

so I know that A looks like 1010 (note that 4 fingers is a good way to remember leftovers!)

You can group 4-bit blocks together, so AA is 1010 1010. To convert the binary back to hex, I go back to base 10 again, adding authority 2. You can do this by forming blocks of 4 bits (padding with 0s ) and a string of results.

therefore, 111011101 is 0001 1101 1101 , which is (1) (1 + 4 + 8) (1 + 4 + 8) = 1 13 13 , which is 1DD