Question

Question II (5 marks) 1. Suppose a computer wants to subtract decimal number 58 from decimal number 70. As we studied, the computer will do this using a method called 2's Complements. a. Show the step by step solution of the subtraction process using 2's Complements for the above given scenario. b. In your own words, describe each step you have done from question (a) above and explain why the step is important for the whole process to be successful. 2. Suppose the subtraction of 58 from 70 is a part of a program code, and the final answer is required in Octal number, a. Show the solution of the conversion on your answer sheet. b. Relate the conversion solution you used in question (a) above to one of the conversion rules that we studied.

Answer 1

Ans 1 (a) and (b)

ans 1 Two decimal numbers are: 58 and 70. hat, b) To perform Suldratt se from to using 2's complement (Both the parts 16a) & (6) (70) 10 (58) io care solued here) step i bonuerti decimal number 70 to binary number. 2 70 For 2's 35-01 complement Binary : 17-1 necessary to convert (1000110), 2 4-0 decimal to 2. 2-0 linary (Importance 2 2 it is 2 1-o of step 1) 2158 step ii) Conuert decimal number 58 to binary member. for 2's complement 2 29-01 it is necessary 2. 14-1 ito convert 2 7-0 decimal no. (111010), 3-L to bimany I- (Importance Binary : - 2 of step uis)

) Now using the method 2's complement : (10)10 + (1000110), for 2's complement : a) 1's.comelement of 1000110 > OITOON b) Now, add 1 in t's complement (for 2 is complement, + first it is necessary OTILO10 to find is complement) (And then add 1 in es complement ~ 111010 i's complement) Now, for (58) 10 (for both to and s8) (58) 10 = (1010), CImportance fou 2's complement of step ii) a) I's complement of 111010 -> 000101 b) Now, cadd I in is complement ܙܘ ܢܘܘܩ +| OOOLLO Y 2's somplement 000110

iv) Now - sulitract (58) 10 froom (10/10 using 2's complement In step civ), sulitract (70) 10 ion is done 1 wing 2's comyloma.it C7010 + (-658) i Crinal step) L2's complement of S8 (58) 10 In binary - + Clinany form of 70) O OLLO (2's comp. of ss) This step is =) 001100 i important to > loo find result luof the sub v awe answer in terms of binney foum is (1100), (final result) consider only 6 digits noolloo vi) for verification :- This is an optional steps done to verify owe result (70)10 - (58) 10 = (12) 10 (12210 in 2. 12_ binary form 8- [(12)70 = (1100), 1 2. 6-0 2 3-0 Hence, verified

In ans 1, I have explained both the parts side by side. Importance of ech step is shown by red pen.

Ans 2 (a)

Answer (2) WK 12 076-28 9 17 MONDAY 8 AM 9 AM 10 AM The given decimal nos 58 and 70 These are decimal numbers so base is 10 (5810 t (70) 10 We have to change (58% into octal no base y octal 20. 8 so elivide this decimal no. 8 58 85817 12 50 11 AM in 12 PM we by 8 1 PM 1 2 PM 3 PM We will divide it till we don't get quotient smaller than This order will be followed to octal number 4 PM 5 PM = 72 6 PM so. (58) = (72, Similarly (70) 7 PM 870 18 EVENING 8170 8 8 61 6 8 Octal no: (1.068 NOVEMBER ОСТОВЕ ST SEPTEMBER ==

octal number 106 so decimal number 70= (7000 (106 g Now calculate subtraction af Octal numbers i (106) & (72Jg we 12 0 م (1068 - (720g 287 Base=8 borrow-8 o 14 6-2=4 o-7 not possible sowe borrow from 1. But This is actal no. so we borrow & 8-10 I will be zero Hence difference of (106) & (12g = 14 Ans: 14 5

Ans 2 (b)

(6) conversion rules WK 12 078-287 19 WEDNESDAY 1 8 Write M the given decimal number ce 58 € 70 9 w 10 II of the given decimal number is less & then octal number is the same 5878 8 7078 T of the decimal number greater then 7 then clivide the number 858 27 8)70 18 56 649 6 12 by 8 - 1 2 mi TV 34 Note the can see remainder in we get after division we ins :: Remaindes in 58= 2 Remainder in 70 = 6 30 VENING مل I repeat step 3 and 4 with the cuotient till it less than 8 In decimal no Quotient is 8 So 8-8 8884 Remainder=0 OUT == DESEASE

So see 8158 12 7 the clivision 81 701 8 To 8 27 z Now write the remainders in reverse order (batton to lop. decimal 8 72 70- ToG VII The resultant is the no to the given elecimal number. (58),= (12g (10) = (1008 Squivalen octal 8