Q&A for How to Convert from Decimal to Hexadecimal

Since every 4 bits in a binary code is 1 hex number, the best thing to do is convert each 4 bits into a decimal number then into a hex number. 1001₂ would be 8 plus 1 which is equal to 9. 0111₂ would be 4 plus 2 plus 1 which would then be 7. The answer is 79₁₆.

Start with number n, for the sake of having an example, let's say 86. Take the number and divide by 16 -> 5R6. If the result of your initial division (not the remainder) is greater than 16, then you must divide that number by 16. In this case, 86dec is equal to 56hex.

This is going to sound stupid, but it might help explain why the algorithm is "obviously" correct: Try using it to convert base 10 to base 10. Pick any number in base 10, say 15069. Divide it by 10. 1506, remainder 9. Divide 1506 by 10. 150, remainder 6. Divide 150 by 10. 15, remainder 0. Divide 15 by 10. 1, remainder 5. Divide 1 by 10. 0 remainder 1. See? It really is obvious. Each time, you're just picking off the least significant digit in whatever base you divide by.

Method 1: Convert to decimal first. 145(octal) = 1x8² + 4x8¹ + 5x8⁰ = 64 + 32 + 5 = 101(dec). Divide 101 by 16 to get 6 + remainder 5, therefore 142(octal) = 65(hex). For the fractional part, 0.02(octal) = 0x(1/8¹) + 2x(1/8²) = 2/64 = 1/32 = 0.03125(dec). Multiply 0.03125 by 16 to get 0.5, which has a whole number part of 0. Multiply 0.5 by 16 to get 8. Put the 0 and the 8 after the (hexa)decimal point to get 0.08(hex). Result = 65.08(hex). Method 2: Convert to binary first. 145.02(octal) = 001 100 101.000 010. Then group into 4-bit nibbles to get 0110 0101.0000 1000. Convert each nibble into hex (see How to Convert Binary to Hexadecimal ) to get 65.08(hex).

98735 is not in base 2. Each digit cannot be larger than the base - 1, so for base 2, the digits cannot be larger than 1. 98735 to binary (base 2) is 11000000110101111. To convert binary to hexadecimal, take each group of 4 bits and convert each to hexadecimal. 0001 1000 0001 1010 1111₂ = 181AF₁₆

4E is 78 in decimal (base 10). 6B is 107₁₀. 78₁₀ + 107₁₀ = 185₁₀. Which is B9 in hexadecimal. You can also do it in hexadecimal: E+B = 14₁₀ + 11₁₀ = 16₁₀ + 9₁₀ = 19(hex). In other words, it is 9(hex) plus a carry of 1. Now add 4 + 7 = 11₁₀ = A, add the carry to give B. The answer is B9.

You first figure out the hex of the positive value, which is 1ef, then for each digit do (15 - digit) so 1ef becomes e10, then add 1 to that hex, e10 becomes e11, then add an f to the beginning. e11 becomes fe11.

In the first step, if the decimal remainder is less than 0.0625 you add at least one 0 to the digit. If there are more than 1 zeros to the right of the period, you count the zeros and subtract 1 and add that many zeros to your digit. Examples: 1,078,160 / 1,048,576 = 1.029. So the first digit is 10. In the next step you still do 1 x 1,048,576, not 10 x 1048576. Another example: 4097 to hex. 4097 / 4096 = 1.000244. There are 3 zeros to the right of the period, so your first digit is 100. 4096 X 1 = 4096. 4097 - 4096 = 1. hex answer = 1001.

Assuming this is binary (if this is decimal, convert it to binary). Split the binary into 4 bit chunks (nibbles): 1000 1101 0100 0110 1111. Convert the nibbles into the hexadecimal: 8D46F.

Start by converting the decimal 1011 to binary: 1111110011. Now break the binary number into nibbles (4 bits/binary digits): 0011 1111 0011. Now convert the nibbles into their respective hexadecimal: 3F3.

Convert it to binary, break it down into 4 bit chunks (nibbles), convert the nibbles into the respective hexadecimal.