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betic character; otherwise returns c. toupper ( >
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int toupper(int c); Returns the uppercase version of c if c is a lowercase alphabetic character; otherwise returns c. <ctype.h>
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AppendixG
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Humans normally use the base 10 numbering system. This is called the decimal system for the Greek word deka for ten. Our ancient ancestors learned it by counting with their 10 fi.ngers. Computers have only 2 fingers (Le., there are only 2 possible values for each bit), so the binary system works well for computers. But the trouble with binary numbers is that their representations require long strings of bits. For example, 1996 is represented as IIIIIOOIIOO in binary. Most humans find long strings like that difficult to process. Binary numbers are easy to convert to other bases if the base is a power of 2. For example, conversion between binary and octal (base 8 = 23) merely requires grouping the binary bits into groups of 3 and interpreting each triplet as an octal digit. For example, to convert the binary numeral IIIIIOOIIOO write ~I,~II,OOI,IOO = 3714. Here, 11 converts to 3, III converts to 7, o o 1 converts to I, and I o o converts to 4. Conversion from octal back to binary is just as simple. For example, 2 6 5 o converts to I o 11 o 1 o 1 o o 0, which is 1448 in decimal. Note that octal numerals use only the first 8 decimal digits: 0, I, 2, 3, 4, 5, 6, 7. After 8, the next power of 2 is 16. Using that base makes the numerals even shorter. This is called the hexadecimal system (from the Greek hex + deka for six + ten ). Conversion between binary and hexadecimal is just as simple as it is between binary and octal. For example, to convert the binary numeral ~OII~OIOIOO to hexadecimal, group the bits into groups of 4 (from right to left) and then translate each group into the corresponding hexadecimal digit: 101,11~1,0100 = 5d4. Here, I o I converts to 5, I I o I converts to 11, and o I o o converts to 4. The hexadecimal digits I 0, I 1, I 2, I 3, I 4, and I 5 are denoted by the first six letters of the alphabet: a, b, c, d, e, f. The output manipulators dec, hex, and act are used for converting different bases:
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EXAMPLE G.1
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This shows how both the value and the address of a variable can be printed:
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. #include <iostream.h> main0 { int n = 1492; // tout << "Base 8: tout << "Base 10: tout c-c "Base 16:
base n = H n = b n = '
10 -CC act CC n CC endl; CC n CC endl; c-c hex cc n C-C endl;
HEXADECIMAL NUMBERS
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Here the manipulator oc t is used to convert the next output to octal form. Note that the output reverts back to decimal until the hex manipulator is used.
The next example shows how to input integers in octal and hexadecimal. Octal numerals are denoted with a 0 prefix, and hexadecimal numerals are denoted with a Ox prefix:
EXAMPLE 6.2 This shows how both the value and the address of a variable can be printed: #include <iostream.h> main0 1 int n; tout << "Enter an octal numeral (use 0 prefix): "; tin >> n; tout << "Base 8: n = ' C-K act << n << endl; tout << "Base 10: n = ' << dec C-C n -CC endl; tout << "Base 16: n = ' << hex -C-C n << endl; tout << "Enter a decimal numeral: "; tin >> n; tout << "Base 8: n = ' << act C-C n << endl; tout << "Base 10: n = ' C-C dec -CC n -C-C endl; tout << "Base 16: n = ' C-C hex -CC n -CC endl; tout << "Enter a hexadecimal numeral (use Ox prefix): "; tin >> n; tout << "Base 8: n = ' -CC act C-C n -CC endl; tout << "Base 10: n = ' CC dec -CC n << endl; tout << "Base 16: n = ' -C-C hex CC n C-C endl;
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