GLOBAL INTITUTE OF TECHNOLOGY

Assingement-I

Digital Electronics Branch: III-CS & IT

UNIT-I

1. Perform the following conversions:a. (43.6) base 10 to binaryb. (182.75) base 10 to binary having 8-bit integer and 5-bit fraction.

2. Determine the radix-2 representation of the integer whose radix-8 representation is 3456.3. A number is written as 275 in radix r number system and 346 in octal number system. What is

the value of radix r?4. Convert 237 to base 3, base 4, base 7 and base 8, number system.5. Perform the following conversion and find x:

a. (4057.06) base 8 = X base 10b. (2598.675) base 10 = X base 16c. (3A9.B0D) base 16 = X base 2d. (2035) base 8 = X base 16

6. Given (16) base 10 = (100) base b find b?7. Subtract 2B9 base H from 1352 base H , show the step followed.8. A number is expressed in binary 2’s complement as 10011. Find its decimal equivalent value.9. Show the 8 bit subtraction of decimal number in 2’s complement representation (-28)-(-65).10. Use 1’s and 2’s complement to perform M-N with the given inary numbers:

a. M=1010100 N=1000100b. M=1000100 N=1010100

11. Use BCD arithmetic to perform the following addition:a. 125+235b. 897+768

12. Subtract the following using 9’s complement:a. 649-387b. 891-786

13. Convert the following excess-3 number in decimal: 0111 1011 1100.14. What do you mean by self complementing and cycle codes? Give one example for each type

code. Convert the binary number 100101 for gray code.15. Find equivalent binary Gray code of (478) base 10.16. Solve the following:

a. (110101) base G = (?) base 2b. (10101101) base 2 = (?) base G

17. For the integer with decimal representation 24567 give the corresponding bit-vecotrs for the BCD code and for the Excess-3 code.

18. Convert the following numbers from the given base to the other base indicated:a. (110111101) base 2 = (?) base 10, (?) base 8, (?) base Hb. (632.25) base 8 =(?) base 10, (?) bae Hc. (2AC5.2B) base 16=(?) base 10, (?) base 8

19. Represent the decimal number 396 in following forms:a. Straight binaryb. BCD codesc. Excess-3 coded. Octal codee. Hexadecimal code

20. Convert the following:a. (AB6) base 16 into decimalb. (AF9.B0D) base 16 into binaryc. (1248.56) base 10 into hexadecimald. (543.26) base 10 into octale. (247.36) base 8 into hexadecimal

21. Represent 4096 in binary form in:a. BCD Codeb. Excess-3 codec. 8-4-2-1d. 7-4-2-1

22. Convert the following:a. 1001.11 base 2 to decimalb. 198 base 12 to decimalc. 2 AC5.D base 16 to decimald. 725 base 10 to binary

23. Represent the decimal number 27 in binary form using:a. Binary Codeb. Gray Codec. Octal Coded. Hexadecimal Code

24. Convert the following numbers:a. 53.625 decimal into binaryb. 64.AB hexadecimal into octalc. 3A9.BOD hexadecimal into binaryd. 4057.06 Octal to Hexadecimal

25. Convert the following numbers:a. Decimal 225 to binary, octal and hexadecimalb. 1938.257 decimal to hexadecimalc. 175.175 decimal to binaryd. Determine the value of base X if: (211) baseX =(152) base 8e. Represent decimal number 8520 in:

i. BCDii. Excess-3 code

iii. 2421 codef. Perform following arithmetic operation:

i. –(205) base 10 + (171) base 10 using 1s complementii. (202) base 10 –(171) base 10 using 2’s complement

26. What is BCD correlation in reference to BCD arithmetic? Give one example.27. Define with example: BCD code28. Write short note on fixed point and floating point arithmetic.29. Define with examples:

a. Weighted and non-weighted codesb. Alphanumeric codes

30. What are the main characteristics of gray code?31. Use 2’s complement method to perform M-N with any binary number.32. What do you mean by self complementing and cycle codes? Give one example for each type of

code. Convert the binary number 100101 for gray code.33. What is BCD correlation in reference to BCD arithmetic? Give one example34. Write short notice on Numbers and Alphanumeric codes.35. Define the following with one example:

a. Sequential codeb. BCD Codec. Excess-3 code

36. Define r’s and (r-1)’s complement37. Find dual of Y=AB+C’D+EF38. Prepare a truth table and logic circuit diagram for the following Boolean expression:

a. A.B + A’.Bb. AB’.C + B’C

39. Prove the following Boolean expressions:a. A + AB =Ab. A+ A’B=A+Bc. (A+B) (A+C)=A+BC

40. Simplify OR prove the following expressions:a. Y= X’(X+Z)+A’+AZb. N=(X1 +X2) +(X +X1 X2)c. A= WXY (WX’ + WY’) + WX’Yd. ((AB’+ABC)’+A(B+AB’))’e. (A+B)((AC)’+C)(B’+AC)’f. (A+B)(A+B)’=(AB +A’B’)’g. (AB’ (C +BD)+A’B’)C=B’Ch. (AB+AC)’+A’B’C=A’+B’C’i. Y= B (A+B’)(B+C)j. Y= A (B+C’(AB +AC’)’)

k. Y=(A+B’C’)’(AB’+ABC)l. Y=(AB’(A+C))’ + A’B (A+B’+C)’m. A(B+C’ (AB+AC’)’)n. AB’C + B +BD’ +ABD’+A’Co. (A’ + (A+B)’) B’ + (B+C)’)p. AB + (AC)’ + AB’C (AB +C)q. (AB’ (A+C))’ + A’B (A+B’+C)’r. Y= AB +(AC)’ +AB’C (AB+C)s. Y=((AB+C’)+ ((A+B)’ +C))’t. A’B’ +AB +A’B =A’+Bu. AB’ +B’C’ +A’C’ =AB’ +A’C’v. F =(BC’ +A’D)(AB’+CD’)w. F=((AB)’A) ((AB)’B)x. (A’+ (A+B)’) (B’ + (B+C)’)y. (A’B) + A’ +ABz. (A+B)’ A’ (A+B)

41. Find the complement of f +x +yz then show that f.f’ =0 and f +f’=142. Using Boolean Algebra prove that AB + BC +A’C = AB +A’C43. Explain how positive logic NAND gate is equivalent to negative logic NOR gate44. Find the logical operation performed by a gate whose voltage truth table under positive logic

system is:

A B Output-5V -5V 0 V-5V 0 V -5V0 V -5V -5V0 V 0 V -5V

45. Find dual of Y =AB +C’D +EF46. Simplify the following Boolean expression to a minimum number of literals:

a. XY’ +X’Y +YX +(XY)’b. ((XYZ + (XY)’ )’+ YZ)’c. ABC + A’B +ABC’d. (BC’ +A’D) (AB’+CD’)e. (AB)’ + AB +A’Bf. AB’C +B +BD’ +ABD’+A’C

47. State and prove the two basic De Morgan’s theorems.48. Write short note n universal gate. Implement the XOR gate using minimal number of NAND

gates. Show that the circuit drawn realizes the XOR gate.

UNIT-III

1. Express the function Y =A +BC in a. Canonical SOP formb. Canonical POS form

2. Simplify F =(A+B) )A+C’) (A’ +B’) into sum of product form.3. Give the logic equation F= ABC + BC’D +A’BC

a. Make a truth tableb. Simplify using K-Mapc. Realizing using NAND gated only

4. Using the K-map for four variables A, B, C, D simplify the following expression and draw the equivalent logic gates circuit:

a. Y= m1 +m3+ m5+ m7 +m8 +m9 +m12 +m13b. Y= A’B’D’ + ABC D’ +B’ CD +AB C’ + BCDc. F(A, B, C, D)= ∑m (0,1,2,3,5,7,8,9,11,14)d. F(A, B, C, D)= ∑m (0,2,4,5,6,8,10,13,15)

5. Use K-map to simplify the following expression and realize logic circuit using NAND gatef= ∑m (0,2,3,4,6,8,9,11,10)+ ∑d(12,14)

6. Simplify the following Boolean function using K-mapa. F(A, B, C, D)= ∑ 4,6,7,15)b. F(A, B, C, D)= ∑m (0,2,4,5,6,7,8,10,13,15)

7. Obtain minimal SOP expression using Karnaugh mapf= ∑m (1,5,7,13,14,15,17,18,21,22,25,29) + ∑d (6,9,19,23,30)

8. Use K-map to obtain POS form of given expression:F =B’C’ + A’B’ + ABC

9. Minimize the following logic function using K-maps and realize using universal gatesF(A,B,C,D)= ∏M (0,3,4,5,6,10,11,14,15)

10. Using K-map method simplify the following Boolean function and obtain:a. Minimal SOP form b. Minimal POS form

Y= ∑m (0,2,3,6,7) + ∑d (8,10,11,15)11. Using K-map minimize the function given in following form obtaining sum of product form

F= ∏M (4,5,6,7,9,13)Simplify the following Boolean Expression using K-map and verify it using the Quine-McClisky method: Y (A,B,C,D)= ∑m (0,1,3,7,8,9,11,145)

12. Illustrate the Quine-McClisky tabula method for obtaining minimum sum of the product form the following four input function:

f= ∑m (0,1,3,5,7,11,12,13,14)13. Use the tabulation procedure to generate the set of prime implicants and to obtain all minimal

expression for the following function:F(w,x,y,z)= ∑m (0,1,4,5,6,7,9,11,15) + D(10,14)

14. Express the following function in canonical sum of minterms and product of maxterms

F= Y’Z’ +WXY’ + W X’Z’ +WX Z’ W’Z’X’15. A staircase light is controlled by two switches at the top and another at the bottom of stairs:

a. Make a truth table for this system.b. Write logic equation in SOP form.c. Realize the circuit using AND –OP gate.d. Realize the circuit using NAND.

16. Express the following functions in canonical sum of minterms and product of maxterms

F = (A+B’+C)(A+B’) (A+C’+D’)(A’+B+C+D’)(B+C+D’)

17. Write short note on Karnugh map.18. Write short note on incomplete specified functions.