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Practice Assignment No-
Subject: Digital Logic Design Course: BEE-2 CD Issue: 05 Mar 2012
Note:
This practice assignment aims to enhance student’s problem
solving skills and build their design conceptions.
The students are expected to solve these problems in their own
time and discuss with the teacher, if required.
Problem No-1 Which of the following are analog quantities, and which are digital? a. Number of atoms in a sample of material b. Altitude of an aircraft c. Timer setting on a microwave oven d. Temperature of a room e. Automobile fuel gauge
Problem No-2 Perform the following conversions:- a. 757.25 10 to Hexadecimal, Octal, and binary. b. 3BA.25 14 to base6.
Problem No-3 Add, subtract, and multiply:- a. 1111 and 1001 b. 110010 and 11101
Problem No-4 Divide in binary:- 110000011 and 1011
Problem N0-5 Convert the following signed decimal numbers to BCD and perform addition and subtraction:- a. -97 10 and +965 (^10)
Problem No-6 Complete each expression:- a. a′.0= b. w′(wxyz)′= c. (x′+x′)′= d. x≡xy= e. f[a,b,(ab)′]= f. f[a,b,ab]= for e and f, use f(a,b,c)=a+b+c
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Problem No-7 Prove the identity of the following Boolean equations, using algebraic manipulation:- a. AB+BĆD́+ÁBC+ĆD=B+ ĆD b. WY+ẂYŹ+WXZ+ ẂXÝ=WY+ ẂXŹ+X́YŹ+XÝZ
Problem No-8 Reduce the given Boolean expressions to the indicated number of literals:- a. X+Y[Z+(X+Z)′] to two literals b. (AB+ÁB́)(ĆD́+CD)+(AC)́ to four literals
Problem No-9 Find the complement of the following expression by (1) duality and (2) DeMorgan’s Law:- F=(V′W+X)Y+Z′ Then Show that FF΄=0 and F+F΄=1.
Problem No-10 Convert the following to the sum-of-minterms canonical form:- a. F(A,B,C)=(A′+B)(B′+C) b. F(w,x,y,z)=π(0,1,2,3,4,6,12)
Problem No-11 The logical sum of all the minterms of a Boolean function of n variables is 1. a. Prove the previous statement for n=3. b. Suggest a procedure for a general proof.
Problem No-12 By substituting the Boolean expression equivalent of the binary operations as defined in Table 2.8 of your text book, show the following:- a. The implication operation is neither commutative nor associative. b. The exclusive-OR operation is commutative as well as associative.
Problem No-13 Convert the given expressions into indicated forms:- a. (a+b+c+d΄)(b+c+d)(b΄+c΄) Sum-of-Product(SOP) b. wxy΄+xy΄z+wx΄z΄ Product-of-Sum(POS)
Problem No-14 Write the Boolean expression for the output of Figure P14a, and use it to determine the complete truth table. Then apply the waveform of Figure P14b to the circuit inputs, and draw the resulting output waveform.
