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METU Northern Cyprus Campus

EEE-248/CNG-232 Logic DesignFall 2014

Homework #1due on October 16th(100 pts)

Please submit your solutions to this homework electronically through ODTUCLASS.

1.

(8) Perform the following operations in binary number system:

a)

1101.010 + 10.11 b) 1101.0110.101 c) 101.1 x 11.101 d) 1101.11101.1

2.

(6 pts) Show the binary representation of the following decimal numbers in (i) 2s complement, (ii) 1s

complement, using 20 bits:

a)

169,000 b) -139,999 c) - 6

3.

(6 pts) Convert the following unsigned binary number to a) hexadecimal, b) octal, and c) decimal,

rounding fractional part to 4 digits in your answer:

1011011101.110101

4.

(4 pts) Convert the following hexadecimal number to binary, and then to octal: BCAF

5.

(6 pts.) Convert the following decimal number a) first to binary, and b) then to base 12, rounding

fractional part to 4 digits in both cases: 2041.873

6.

(4 pts) Determine the base xof a number system such that unsigned 2E1(16)= 2102(x)

7.

(12 pts.) Consider the 12 bit signed 2s complement binary numbers A= 0101 1111 0100 and B = 1100

1101 1001. Perform the following operations, and note if there is an overflow:

a)

A+B b) A-B c) B-A d) -A-B

8.

(6 ps.) A computer can store 3 decimal digits. How is the number 791 stored in each of the following

codes (hint: consider each digit separately in all cases as in BCD examples):a)

8421 b) 5421 c) excess 2

9.

(6 pts) Assume the following binary information contains text encoded in 8-bit ASCII. Translate it into

English:

011011000110111101110110011001010010000001101000011011110110110101100

1010111011101101111011100100110101100100001

10.

(6 pts.) For each of the following functions find a minimum SOP expression. Show each algebraic step:

a)

f = ab + abcd + abcd

b)

g = ce(a+b+c+e)(b+c+d+e)(a+b+c+e)

11.

(6 pts.) Using the boolean theorems and identities covered in lectures reduce the following expressions

to a minimum SOP form (show each step):

a)

f= xyw + xyw + xyw + xyw + xyw + xyw b) g = ab + bcd + abc + abd + bc + abc

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12.

(14 pts.) For each of the following functions:

f(a,b,c) = m (1,3,5,6) g(a,b,c) = M (1,3,4)

a)

(2 pts) Show the truth table.

b)

(2 pts) Show an algebraic expression in sum of minterms form.

c)

(2 pts) Show a minimum SOP expression.

d)

(2 pts) Show the minterms of f and g (complement of f and g) in numeric form.

e)

(2 pts) Show an algebraic expression in product of maxterms form.

f)

(2 pts) Show a minimum POS expression.g)

(2 pts) If each AND, OR, and NOT gate costs the same amount, which of the functions (f or g) in

part c and part f has the least hardware cost? Explainyour answer.

13.

(6 pts.) Simplify the following Boolean function using algebraic manipulations:

edcbacdcebadcdebabecaf

'''

14.

(10 pts.) Given the following three Boolean functions:

F1= yz+ x ; F2= (x + z)+ x.y + xyz ; F3= F1.F2+ F1.F2a)

(3 pts.) Fill in the provided truth table columns.

b)

(2 pts.) Show the sum of minterms expression corresponding to F3.

c)

(2 pts.) Simplify F3 into a reduced sum of products form.

d)

(2 pts.) Simplify F3 into a reduced product of sums form.

e)

(1 pt.) Draw the logic schematic of reduced F3from part (c).

x y z F1 F2 F3

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1