A23 = 1010 0010 0011 BEE = 1011 1110 1110 70C558 = 0111 0000 1100 0101 0101 1000
You can also think of this as the counting systems “flipping over” to another digit at the same time. Hexadecimal counts “. . . D, E, F, 10” at the same time binary counts “1101, 1110, 1111, 10000”.
Each digit in a decimal number is in a certain “place. " Moving from right to left, there’s the “ones place,” “tens place,” “hundreds place,” and so on. The digit 3 just means 3 if it’s in the ones place, but it represents 30 when located in the tens place, and 300 in the hundreds place. To put it mathematically, the “places” represent 100, 101, 102, and so on. This is why this system is called “base ten,” or “decimal” after the Latin word for “tenth. "
Starting with the rightmost digit, 7 = 7 x 100, or 7 x 1 Moving left, 3 = 3 x 101, or 3 x 10 Repeating for all digits, we get 480,137 = 4x100,000 + 8x10,000 + 0x1,000 + 1x100 + 3x10 + 7x1.
116 = 1 x 160 = 1 x 1 (All numbers are in decimal except where noted. ) 216 = 2 x 161 = 2 x 16 916 = 9 x 162 = 9 x 256 C = C x 163 = C x 4096
A = 10 B = 11 C = 12 (We’ll use this on our example from above. ) D = 13 E = 14 F = 15
C92116 = (in decimal) (1 x 1) + (2 x 16) + (9 x 256) + (12 x 4096) = 1 + 32 + 2,304 + 49,152. = 51,48910. The decimal version will usually have more digits than the hexadecimal version, since hexadecimal can store more information per digit.
3AB16 = 93910 A1A116 = 4137710 500016 = 2048010 500D16 = 2049310 18A2F16 = 10091110
Counting from zero upward: Hexadecimal Decimal Hexadecimal Decimal 0 0 10 16 1 1 11 17 2 2 12 18 3 3 13 19 4 4 14 20 5 5 15 21 6 6 16 22 7 7 17 23 8 8 18 24 9 9 19 25 A 10 1A 26 B 11 1B 27 C 12 1C 28 D 13 1D 29 E 14 1E 30 F 15 1F 31
