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digital logic design
( i have a lot questios so please help me)

Proof that:
A¡¦.B + B¡¦.C¡¦ + A.B + B¡¦.C = 1

Q3 [2 points], According to DeMorgan theorem, the complement of
W . X + Y . Z is W¡¦ + X¡¦ . Y¡¦ + Z¡¦

Yet both functions are 1 for WXYZ = 1110. How can both function and its complement be 1 for the same input combination? What is wrong here?

Q4 [2 points], Write a truth table for the following logic function:
F = A¡¦ . B . (C . B . A¡¦ + B . C¡¦)

Q5 [3 points], List the octal and hexadecimal numbers from 16 to 32. Using the last A, B, C for the last three digits, list the numbers from 8 to 28 in base 13

Q6 [6 points „» each 1.5 point], Do the following SHOW YOUR WORK (IF YOU DO NOT SHOW YOUR WORK YOU WILL EARN ZERO MARK):

b)(27.315)10 =( )2= ( )8

c)What would be the base of the number system if (BEE)r = (2699)10

d)(1.10010)2 = ( )10 = ( )16

Q7 [5 points], Do the followings:
a) Perform the subtraction on the given unsigned numbers using 10¡¦s complement subtraction of the subtrahend (SHOW YOUR WORK)
(125-1800) , (6428 - 3409)

b) Perform the following operations in 10¡¦s complement
(-9286) + (+801) , (-9286) + (-801)

c) [2 points] Convert the decimals +49 and +29 to binary, using the signed-2¡¦s complement representation and enough binary digits to accommodate the numbers. Then perform the binary equivalent of (+29) + (-49) , (-29) + (-49)

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