Question

P7.20. Perform these operations by using eight-bit signed two's-complement arithmetic: a. 17 10 + 15 10; b. 17 10 - 15 10; C. * 33 10 - 37 10; d. 15 10 - 63 10 : e. 49 10 - 44 10.

Answer 1

We have used 2's complement arithmetic rules to solve the problems.

(9) + (12) To 10 (15), Any Positive number is a's complement represented by normal binary number with ms B (most significant bit) 0. oooloool is lo (7), (15) 10 - 001111 + 00100000 = 00010001 lo Now (b) (17), We have to reforesent -(15),o into binary using 2's complement. So first represent +(15)10 and takes a's of it. (15), 50000llll For a's complement ta ke I's Complement and add 1 to it (15). 11110000 11110001 (-15), Now ooo 10ool (17), (-15), 110001 1: Discard the carry 00000010 00000010

(0) (33)10 (37)10 (33), = 00100001 (-37), in a's complement (37) 10 = 001001ol (31), = 110 11010 (1's complement) 11011011 Cats Complement 0010000 (33) 10 2 637)10 511011011 11111100 No is MSB is 1 carry generated and so its a negative number, take a's complement of sum. 00000011 00000100 (magnitude) Final Ans (4) 10

(4) م (5)) - (43) 0 0 0 0/7) و (5) هر (63) 2 |||||| 10 و (13) | | 0 0 0 0 0 0 ( 1 ) (2 100000| (3) (15) = 0 0 0 0 ||| ) مر(63) 7 | | 000 00 ( )00000 و او tale No carry answer is complement for magnitude negative, |||01| 0 م م ه مه || On و((18 ) 0 )o 0 0 1 0 0 0 |

이 (5) (0100000 Final Answer Discard it carry 기 lolQ 0 0 0 0 1) al a 19 | | C 이(H) - (C) 0 0 || 2012 (l 1100|0|| - 이 hhㅋ ( 09 ll Oloo = Guy) 100 0 1100 이 (h) 이(n) - (b) (e)