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### G.2. Relationship between Binary, Octal, and Hexadecimal Numbers

From Table G.1 we see that 3 bits are needed to represent any octal digit, and 4 bits to are needed to represent any hexadecimal digit. We can use this fact to convert between binary, octal, and hexadecimal systems, as shown in Figure G.1.

##### Figure G.1. Converting between Binary, Octal, and Hexadecimal

The procedure for converting an octal to a binary is shown by the arrow marked (a). We can prove that replacing each octal digit by its 3-bit equivalent binary value gives the right result:

 1738 = 1×82 + 7×81 + 3×80 = 1×(23)2 + 7×(23)1 + 3×(23)0 = 1×26 + 7×23 + 3 = (0012)×26 + (1112)×23 + (011 ...

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