Question

a) Calculate the 273 – 278 in 2’s Complement Binary number.


b) (740)8= ( ? )16​

Answer 1

Answer:

a) Calculate the 273 – 278 in 2’s Complement Binary number.

b) (740)8= ( ? )16​

Explanation:

Answer 2

calculate 273-278 in 2's complement and convert (740)8 to hexa-decimal

Explanation:

1. To determine 2's complement of a decimal number we first convert it to binary, take it's 1's complement(complement each bit) and add 1 to it(binary addition). 2's complement of a positive decimal number is simply its binary conversion.
2. here we have , $273-278 = 273+(-278)\ \ \ \ ---(a)$                                              
3. here we two decimal numbers first convert them to binary,                                    $(273)_{10}=(100010001)_2$                                                                                                    for negative number we do 2's complement using point 1. ,                                     $|-278|=278 \\(278)_{10}=(100010110)_2\\1's\ complement\ - 011101001\\adding\ 1 - 011101010 =(-278)_2$            
4. from (a) we get ,        $273+(-278)= 100010001+011101010$                                                                                                          

                                                                 $=111111011$       --(b)  

   5. here (b) is in 2's complement form hence, left most bit shows sign of

       the  number in decimal form ,                                                                                      

                                         $111111011\ \ \ ->negative \\1's\ complement, 000000100\\add\ 1, 000000101\\convert\ to\ decimal, (101)_2=(5)_{10}$                                              

        hence, $273-278=-5$          

    6. converting octal to hexadecimal we first convert octal to binary and  

        then binary to decimal.             $(740)_8= (111100000)_2$                                          

     7.To convert binary to hexadecimal we make bits multiple of four and

         divide them in groups,                                                                                            

                             $(740)_8= (000111100000)_2\\groups\ of\ 4,\ (0001\ 1110\ 0000)\\(0001)_2=(1)_{16},\ \ (1110)_2=(E)_{16},\ \ (0000)_2=(0)_{16}$  

     8. hence, $(740)_8=(1E0)_{16}$