1. Integer Types

2. Bits and bytes A bit is a single two-valued quantity: yes or no, true or false, on or off, high or low, good or bad One bit can distinguish between two cases: T, F Two bits can distinguish between four cases: TT, TF, FT, FF Three bits can distinguish between eight cases: TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF In general, n bits can distinguish between 2 n cases A byte is 8 bits, therefore 2 8 = 256 cases

3. Number systems The binary (base 2) number system uses two “binary digits, ” (abbreviation: bits) -- 0 and 1 The octal (base 8) number system uses eight digits: 0, 1, 2, 3, 4, 5, 6, 7 The decimal (base 10) number system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 The hexadecimal, or “hex” (base 16) number system uses sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

4. Everything is a number? Everything in the computer is stored as a pattern of bits –Binary distinctions are easy for hardware to work with Numbers are stored as a pattern of bits –Computers use the binary number system Characters are stored as a pattern of bits –One byte (8 bits) can represent one of 256 characters So, is everything in the computer stored as a number? –No it isn’t, it’s stored as a bit pattern –There are many ways to interpret a bit pattern

5. Counting To count up in any number system, –add 1 to the rightmost digit –if the result is higher than the largest digit, set that digit to zero and carry to the next place repeat addition of 1 and carrying as many times as necessary Example: In hex, 4A6FF + 1 = 4A700

6. Computers use binary numbers People like to use decimal numbers Computers use binary numbers –Java translates decimal numbers into binary –The computer does all its arithmetic in binary –Java translates binary results back into decimal You occasionally have to use numbers in other number systems

7. Using octal and hex numbers Computers use binary, but the numbers are too long and confusing for people--it’s easy to lose your place Octal or hex is better for people Translation between binary and octal or hex is easy –One octal digit equals three binary digits 101101011100101000001011 5 5 3 4 5 0 1 3 –One hexadecimal digit equals four binary digits 101101011100101000001011 B 5 C A 0 B

8. Writing octal and hex integers Integers are usually written in decimal notation: 7, 532, -28 To write a number in octal, just start with a zero: 02, 0657, -077 –but don’t use the digits 8 or 9 ! To write a number in hexadecimal, start with 0x or 0X : 0xA, 0X43AB5, -0xFFFF –the “digits” A through F can be upper or lower case

9. Integer types There are four integer types –byte – occupies one byte (surprise!) can hold numbers in range –128 to 127 –short – occupies two bytes can hold numbers in range –32768 to 32767 –int – occupies four bytes can hold numbers up to + or – 2 billion –long – occupies eight bytes can hold numbers up to about 19 digits literals are written with a L suffix: 123456789L

10. Floating-point literals Floating-point literals are written with a decimal point: 8.5 -7.923 5.000 Floating-point numbers may also be written in “scientific notation”– times a power of 10 We use E to represent “times 10 to the” Example: 4.32E5 means 4.32 x 10 5 float literals are written with a F suffix –Examples: 8.5F -7.923F 5.000F 4.32E5F –If you don’t have the F suffix, type double is assumed

11. Floating point types There are two floating-point types –float – occupies four bytes Can hold numbers in the range 3.4E38 to 1.4E-45 Accuracy is about nine digits –double – occupies eight bytes Can hold numbers in the range 1.7E308 to 4.9E-324 Accuracy is seventeen or eighteen digits

12. Number “width” Numeric types are considered wider or narrower than other numeric types –This is based partly on number of bytes occupied –Also based on how large a number it can hold Java doesn’t mind if you assign a narrow value to a wide variable: int n = 3; Java is not happy if you assign a wide value to a narrow variable: byte b = 7139946;

13. Widening and narrowing You can always assign a narrower value to a wider variable –This is called widening You can do something special to assign a wide variable to a narrower variable –This is called narrowing double float long int short byte

14. Casts You can convert (cast) one numeric type to another When you widen, no explicit cast is necessary –But it doesn’t hurt When you narrow, an explicit cast is required –This requirement is made to help avoid errors Casting tells Java that the value in the wider type will fit in the narrower type Java checks to make sure that the cast works, and gives you an error if it didn’t

15. Example casts short s = 0; int i = 0; double d = 0.0; d = i; // legal d = s; // legal i = s; //legal i = d; // illegal s = d; // illegal s = i; // illegal i = (int) d; // legal s = (short) d; // legal s = (short) i; // legal d = 3.7E20; i = 50000; // The following give // runtime errors: s = (short) i; i = (int) d;

16. The End