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For example, the Intel 80×6 chip set interprets the bit pattern 1001 0101 as an instruction. You certainly can translate this into decimal (149), but that number per se has no meaning. Sometimes the numbers are instructions, sometimes they are values, and sometimes they are codes. One important standardized code set is ASCII. In ASCII every letter and punctuation is given a 7-digit binary representation. For example, the lowercase letter a is represented by 0110 0001. This is not a number, although you can translate it to the number 97 (64 + 32 + 1). It is in this sense that people say that the letter a is represented by 97 in ASCII; but the truth is that the binary representation of 97,01100001, is the encoding of the letter a, and the decimal value 97 is a human convenience. |
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Because binary numbers are difficult to read, a simpler way to represent the same values is sought. Translating from binary to base 10 involves a fair bit of manipulation of numbers; but it turns out that translating from base 2 to base 16 is very simple, because there is a very good shortcut. |
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To understand this, you must first understand base 16, which is known as hexadecimal. In base 16 there are sixteen numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. The last six are arbitrary; the letters AF were chosen because they are easy to represent on a keyboard. The columns in hexadecimal are |
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To translate from hexadecimal to decimal, you can multiply. Thus, the number F8C represents: |
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F * 256 = 15 * 256 = 3840
8 * 16 = 128
C * 1 = 12 * 1 = 12
Total 3980 |
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Translating the number FC to binary is best done by translating first to base 10, and then to binary: |
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F * 16 = 15 * 16 = 240
C * 1 = 12 * 1 = 12
Total 252 |
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Converting 25210 to binary requires the chart: |
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