Hex to Decimal Conversion?

The Asker requested a method by hand to convert from Hex to Dec. So,

(Step 1) Understand what each hexadecimal digit stands for. The digits 0 through 9 stand for their decimal counterparts, while A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.

(Step 2) Count the digits in the hexadecimal number you wish to convert. For example, the hexadicimal number A980C has five digits. Make a list of the decimal equivalents of each the five digits. For example, A980C becomes {10, 9, 8, 0, 12}.

(Step 3) Multiply each number in the list by successive powers of 16, starting with 160 = 1 for the rightmost element of the list. For example, 12 is the rightmost element of our list, so we obtain:

10(16^4) = 10(65536) = 655360

9(16^3) = 9(4096) = 36864

8(16^2) = 8(256) = 2048

0(16^1) = 0(16) = 0

12(16^0) = 12(1) = 12

(Step 4) Add the numbers you obtained in Step 3. This is the decimal equivalent of the hexadecimal number. For example, 655360 + 36864 + 2048 + 0 + 12 = 694284

So, for your first example: 0xC4630000

12(16^7) = 12(268435456) = 3221225472

4(16^6) = 4(16777216) = 67108864

6(16^5) = 6(1048576) = 6291456

3(16^4) = 3(65536) = 196608

0(16^3) = 0(4096) = 0

0(16^2) = 0(256) = 0

0(16^1) = 0(16) = 0

0(16^0) = 0(1) = 0

3221225472 + 67108864 + 6291456 + 196608 = 3294822400

Can you do the other? =) Hope that helps.

Rob is correct if you want to convert from hex (base 16) to dec (base 10).

The zeros at the end of the hex number are placeholders. Just like how you learned to count. 1 is equal to 01 because the zero represents the ten's column and the 1 represents the one's column. But 01 is not equal to 10 because in the former the 1 is in the one's column and in the latter it in the ten's column. So 0x0C000000 is equivalent to 0x00C000000 or 0x000C000000 etc but 0x0C would be much less in value. The trailing zeros are what increasess the value of the number.

If you want to convert hex to single precision floating point the conversion is similar. I assume single precision because you have 32 bits (the leading zero of 0C000000 is padding to indicate eight hex bits; 8*4 = 32)

For 0x0C000000 to single precision floating point:

0 hex is 0 dec is 0000 binary

C hex is 12 dec is 1100 binary

so 0x0C000000 is 0000 1100 0000 0000 0000 0000 0000 0000 b

which can be broken up into:

0 (the sign bit)

000 1100 0 (the exponent)

000 0000 0000 0000 0000 0000 (the mantissa)

sign = 0

exponent = 24

mantissa = 0

The floating point number can be calculated by (-1 ^ sign) * 2 ^ (exponent - bias) * (1 + mantissa)

where the bias for single precision is 127.

So (-1 ^ 0) * 2 ^ (24 - 127) * (1 + 0) = (1) * 2 ^ (-103) * (1) = 9.8607613 E -32

Your other number 0xC4630000 (converting each hex bit to binary):

1100 0100 0110 0011 0000 0000 0000 0000

sign = 1

exponent = 100 0100 0

mantissa = 110 0011 0000 0000 0000 0000

sign = 1

exponent = 136

mantissa is a little more difficult. Each bit uses inverse incrementing powers of 2. Bit 23 has value 1/2 (i.e. 2^ -1), bit 22 has value 1/4 (i.e. 2^ -2) etc. So the mantissa is 2^-1 + 2^-2 + 2^-6 + 2^-7 = 0.7734375

So the floating point number is (-1 ^ 1) * 2 ^ (136 - 127) * (1 + 0.7734375) = (-1) * 2 ^ (9) * (1.7734375) = -908.0

The windows calculator on your computer will convert nicely.

http://www.videojug.com/film/how-to-convert-hexade...