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Baljit · Accepted Answer

COMPUTER ARCHITECTURE
1.   
a) 100100100001110 base 2 to base 3 by division
Now we have to convert binary number to octal number by division. For that we have to first convert binary to decimal number. Then divide resulting decimal number with 8.
Step 1: binary to decimal :multiply nth with 2n-1
1*214+0*213+0*212+1*211+0*210+0*29+1*28+0*27+0*26+0*25+0*24+1*23+1*22+1*21+0*20
=214+211+28+23+22+2=16384+2048+256+8+4+2=(18702)10
Step 2:- Now we will use division method divide decimal number with 8
So Our Result is (44416)8
   
b) 0xC72 to binary
Step 1:Hexadecimal to decimal :-Multiply nth term with 16n-1
         C*162+7*161+2*160=12*256+7*16+2=3072+112+2=(3186)10
Step 2: Divide decimal number with 2
So our Result is (110001110010)2
2.       a)         substraction using 10’s compliment
                   145-129
                   
   Take 10’s compliment of 129 i.e (999-129)+1=871
  145
+871
——
 1016
Now 4th digit represent the carry which mean our result will be positive Number
Now discard the carry our result is  016 i.e 16 
b)  129-145
Take 10’s compliment of 145 i.e. 999-145+1=855
  Now add 10’s compliment of the 145 to 129
 
      129
    +855
     ——
      984
Now there is no carry it means result will be negative so take 10’s compliment of the 984.
(999-984)+1=16
So our result is  -16
3. Given binary integer are signed to msb represent sign if msb is 0 then number is positive if msb is 1 number is negative
a. 000111-001100
  000111
 -001100
————
Take 2’s Complement of 001100 i.e (111111-001100)+1=110100
Now add 2’s complement into first number
  000111
+110100
————
 111011
Now there is no carry so number is negative so take 2’s complement of result
(111111-111011)+1=000101
So our result is -000101
b.   000111-101011
  000111
 -101011
————
Take 2’s Complement of 101011 i.

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