INTERNATIONAL ISLAMIC UNIVERSITY ISLAMABAD
FACULTY OF ENGINEERING & TECHNOLOGY
DEPARTMENT OF ELECTRONIC ENGINEERING
Class : BSEE Digital Logic Design AssignmentNo.01
- What is the exact number of bytes in a system that contains
(a) 32K bytes, (b) 64M bytes (c) 6.4G bytes?
ANS: (a) 1Kbytes=2^10=1024bytes => 32*1024bytes=32768bytes
(b) 1Mbytes=2^20=1048576 => 64*1048576bytes=67,108,864
(c) 1Gbytes=2^30=1,073,741,824 => 6.4 x 2^30byte = 6,871,947,674 byte
- Convert the following numbers with the indicated bases to decimal:
(a) (4310)5 (b) (198)12 (c) (435)8
Ans: (a) 4*5^3 + 3*5^2 + 1*5^1 + 0*5^0 = 500 + 125 + 5 + 0=630
(b) 1*12^2 + 9*12^1 + 8*12^0=140
(c) 4*8^2 + 3*8^1 + 5*1^0=256+24+5
- What is the largest binary number that can be expressed with 16 bits? What are the equivalent decimal and hexadecimal numbers?
Ans: Largest Binary number: 0b1111 1111 1111 1111
Eq. Binary n Hexadecimal: 0xFFFF=2^16-1= 65535
- Determine the base of the numbers in each case for the following operations to be correct:
(a) 14/2 = 5 (b) 54/4 = 13 (c) 24 + 17 = 40.
Ans: (a) (1*x^1+4*x^0)/(2*x^0) =5*x^0
(x + 4)/2=5 => x + 4=10 => x=6
(b) (5*y^1 + 4*y^0)/4*y^0 =1*y^1 + 3*y^0
(5y+4)/4=y+3 => 5y+4=4y+12
=> y=8
(c) (2*z^1 + 4*z^0) + (1z +7*z^0) = 4*z^1 + 0*z^0
=> (2z+4) + (z+7)=4z+0
=>3z +11 = 4z => z=11
- The solutions to the quadratic equation x2 - 11x + 22 = 0 are x = 3 and x = 6. What is the base of the numbers?
X^2 -11X +22= X^2 –(6 + 3)X +(6.3)
ð 1a+1 = 6 + 3
ð a=8
- Convert the hexl number 64CD > binary, and then convert it from binary > octal.
- Convert the decimal number 431 to binary in two ways:
(a) convert directly > binary;
(b) convert first > hexadecimal and then from hexadecimal > binary. Which method is good?
