williams-et-al-1983-apple-ii-computer-graphics

APPENDIX 1-DECIMAL, HEX, AND BINARY 173column which falls into the bit bucket that is ignored anyway. This is whythe two's complement can be used as if it were a negative number, whenit really is not.If you add any number to its corresponding negative value (five plusnegative five) you will always get zero. The same thing happens when youadd any binary number to its two's complement ... almost. Try adding! (3(31(3 (31(31and its complement:! 11(31 1(311You will get all zeros, except for the fi nal carry which falls into the bucket.So we always expect that carry, and ignore it when it occurs.Figure A 1-8 shows another sample of subtraction using two's complement.1 !101 1 001 1 8 !1011 001 1!01 10 1100 - !1001 001 1 - + !1001 0100!0100 01 11Figure A1-8.Notice that it is always the number being subtracted which is changed toits two's complement form. !©1 1© 11©© is changed to !1©©1 ©©1 1, and thena 1 is added to get !1©©1 ©1©©. This number is then added to !1©1 1 ©©1 1to get !©1 ©© ©1 11, and as usual we ignore the bit in the bucket.Negative AddressesThe two's complement essentially changes a number to its negative equ ivalent,so instead of subtracting a number you end up adding its negative.In a decimal setting you can think of it as changing the subtraction 9-3into the addition 9 + (-3) and the result is six in either case.The same idea lets some addresses be written in negative form for convenience.When you wish to enter Monitor from BASIC you CALL theaddress -151. The true address for the Monitor entry point is 65385, and-151 is the two's complement of that address. If you convert 151 to its twobytebinary form (!©©©© ©©©© 1©©1 ©1 11) and take the two's complement(to account for the negative) you get !1111 11_1 1 ©1 1© 1©©1 . The not-soquickconversion to decimal results in the expected value of 65385. Youmust admit that -1 51 is much easier to remember that 65385.Another reason for using the two's complement, or negative, fo rm for