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Extra info for Peace Corps Tunisia - Situation Course
But it works. It works because a special system for representing negatives is used, and because a register has a finite size, like an odometer. 3 Odometer Arithmetic An odometer is an adding machine. It adds up the miles t h a t you drive. Mileage is always considered to have a positive value. ) However, consider the following equation, which we would ordinarily think of as making sense only for negative numbers. x + 10 = 5 42 Chapter 3 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 Logic Circuits and Computation 99,999 99,998 99,997 99,996 99,995 99,994 99,993 99,992 99,991 99,990 99,989 99,988 etc.
It proceeds until a zero quotient is obtained. 4. 4 The Binary System 13 The Binary System Knowing the binary system is important because the native arithmetic of all existing computer processors is binary arithmetic. Binary numbers use only two digits: O and 1. All binary numbers are constructed from just these two digits. Counting goes like this: 1, 10, 11, 1OO, 101, 110, 111, 1OOO, 1OO1, 1O1O, 1011, 11OO, 1101, 1110, 1111, 10000, 10001, 10010, etc. T h e binary system is a placeholding system.
It is the custom to fill these positions with the letters A, B, C, D, E, and F . So in base sixteen, counting goes like this: 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F , 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, I B , 1C, I D , I E , I F , 20, and so on. 4. There is value in being able to add and subtract in hex. Debuggers generally display registers in hex, and it is handy t o be able to check the arithmetic being displayed without having to convert back to base ten. Addition and subtraction are easy to do in hex if we remember t h a t carrying and borrowing are done with 16.
Peace Corps Tunisia - Situation Course