Suppose the PDP-X was a 20-bit machine that used the 2\'s complement system for

Question

Suppose the PDP-X was a 20-bit machine that used the 2's complement system for representing integers (a) Consider the largest positive integer that could be stored (i) Give its representation in octal (ii) Give its representation in hexadecimal (b) Consider the most negative number that could be stored (iii) Give its representation in octal (iv) Give its representation in hexadecimal (c) Which of your answers, if any, change if the computer used the 1's complement system instead? If appropriate, show the new answers.

Explanation / Answer

The basic formula to find maximum and minimum value in 2's complement is:

A) maximum value

i) 2(20-1)-1=524288-1=(524287)10(in decimal ) ==(1777777)8

ii) 524287 in hexamdeciaml =(7FFFF)16

B) most negative number

i) -(2(n-1))=-219=-(524288)10=(2000000)8

ii) -524288 in hexamdecimal =(FFFFFFFFFFF80000)16

C)negative answer remain same but in posivtive no need to do -1

maximum value in 1's complement =2n-1

220-1=219=524288

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