The TCP/IP Guide  9  Networking Fundamentals       9  Backgrounder: Data Representation and the Mathematics of Computing

Decimal, Binary, Octal and Hexadecimal Numbers 1 2 3 4 Binary, Octal and Hexadecimal Arithmetic

Conversions Between Binary, Octal and Hexadecimal

Okay, let's start with the easy stuff first. Conversion between binary, octal and hexadecimal is very simple, as you may have noticed in the preceding topic, where I introduced them. Each octal digit is three binary digits, and each hexadecimal digit is four binary digits. Thus, to convert from binary to octal or hex, just group the digits, and convert each group into an octal or hex digit. To go the other way, convert each hex or octal digit into a set of bits. Table 3 shows the conversions from each of the octal and hexadecimal single-digit values to binary (with decimal digits thrown in for convenience):

Let’s look at some specific examples using larger numbers:

• Binary to Octal: Suppose we start with the binary number 110101001010. We divide this into groups of three: (110)(101)(001)(010). Each of these, we convert to a number from 0 to 7 (which is easy to do in your head if you practice a bit). The result is (6)(5)(1)(2) or 6512 octal.
  
  
• Hexadecimal to Binary: Let's start with the hex number 0x4D1B. We convert each digit as given in the table above. So, we have 0x4D1B = (0100)(1101)(0001)(1011) or 0100110100011011.

Decimal, Binary, Octal and Hexadecimal Numbers 1 2 3 4 Binary, Octal and Hexadecimal Arithmetic