Digital Logic Design. Midterm #1

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1 The University of Toleo f7ms_il7.fm - EES: Digital Logic Design Stuent Name_ Digital Logic Design Miterm # Problems Points Total 5 Was the eam fair? yes no //7

2 The University of Toleo f7ms_il7.fm - EES: Digital Logic Design Stuent Name_ Problem 3 points For full creit, mark your answers yes, no, or not applicable for all offere choices!. The bit strings shown below are vali representations of negative numbers in the four-bit two s complement representation of negative numbers? yes no not applicable. Shown below is the truth table of a boolean function F(A,). Given net to the truth table is a list of boolean function names. Inicate which names in the list are, an which names are not, the name of the function F(A,). A F(A,) yes no not applicable AND, XNOR, NAND, NOR..3 For the four two-level implementation forms of logic gates shown in the table below, write in the types of logic functions that are implementeby the shown two level combinations. TWO-LEVEL IMPLEMENTATION FORMS Two-level ombination Implemente Function NAND-NOR AND NOR-AND NOR NAND-AND AND-OR-INVERT NOR-NOR OR-AND //7

3 The University of Toleo f7ms_il7.fm - 3 EES: Digital Logic Design Stuent Name_ Problem 4 points Positional representations of the function (i), i=,,3, in various raies are shown in Table. Table function (i) i (i) (i) s ecimal representation 5 eight-bit base-two representation of (i) -(i) 3-4E 6-78 Problem statement Using the values of function (i), i =,,3, emonstrate an ability to:. convert by han the liste values of (i), i =,,3, to ecimal representation;. convert by han the liste values of (i), i =,,3, to eight-bit two s complement representation; 3. perform by han the subtraction of numbers in two s complement representation. Problem Solution For full creit, eplicit emonstration of unerstaning the following solution steps is epecte.. Epress (i), for i =,,3, in ecimal representation, an epress both, (i) an -(i) in the eightbit base-two representation which uses the two s complement notation for negative numbers. 3 Show your computation on the opposite page, an enter the results into Table. Hint#:Direct conversion from octal an heaecimal to binary representation is easier, an shoul be applie. Stuents are avise to avoi an inirect, e.g. octal ecimal binary conversion. No partial creit will be given for a correct conversion from an erroneous ecimal representation.. Using the eight-bit base-two representation an the two s complement notation for negative numbers, show the calculation of the ifference ()-() when only an aer circuit is available. Hint#:This part of the problem is consiere inepenent of the results of calculation performe in part.. No partial creit will be earne for a correct calculation proceure applie to erroneous binary representations of () an -() - whether taken from Table, or calculate inepenently. = () + = -() -5 = 6 Result of calculation uner. to be grae: (a) memory content: (b) overflow flag: //7

4 The University of Toleo f7ms_il7.fm - 4 EES: Digital Logic Design Stuent Name_ Problem 3 6 points Equation (3-) shows an incompletely specifie logical/switching function F (A,,,D) in the ecimal lists of sums-of-minterms an on t cares, representation. F (A,,,D) = Σ(,, 3, 4, 5) + (7, 8, 9,,, 3) (3-) Problem statement Demonstrate an ability to:. erive the Truth table an Karnaugh map representations of F,. use the Karnaugh map metho to erive a minimal number of literals POS epression of F, 3. esign the two-level OR-AND an NOR-NOR implementations of the POS form of function F, as specifie in sections 3.3 an 3.4 below. Hint # For full creit: all equations, all answers to questions, all circuit moels an other graphical representations are epecte to be entere into the space esignate for them; all shown numerical results must be precee by the symbolic an numeric epressions whose evaluation prouces these numerical results. Problem Solution For full creit, eplicit emonstration of unerstaning the following solution steps is epecte. 3. Prepare the truth table an the Karnaugh map representations of the function F an show your results in the space reserve for them in Figure 3-. A D F (a) D A (b) F = A(++D)(+) (c) Figure 3- Representation forms of the function F. (a)f s Truth table. (b)f s Karnaugh map. (c)minimum number of literals POS representation of F. //7

5 The University of Toleo f7ms_il7.fm - 5 EES: Digital Logic Design Stuent Name_ 3. Apply the Karnaugh map minimization metho to erive the Minimum number of literals prouct-of-sums (POS) representation of the function F. Enter the erive algebraic representation of F in the space reserve for Figure 3-(c). 3.3 In the space reserve for Figure 3-(a), prepare a logic circuit iagram of the two-level OR-AND form of implementation of the erive epression 3-(c) of the function F. 3.4 In the space reserve for Figure 3-(b), prepare a logic circuit iagram of the two-level NOR-NOR form of implementation of the erive epression 3-(c) of the function F A A F F D (a) D (b) Figure 3- Two-level implementations of the algebraic epression 3-c of function F. (a) OR-AND implementation. (b)nor-nor implementation of F. //7

6 The University of Toleo f7ms_il7.fm - 6 EES: Digital Logic Design Stuent Name_ Problem 4 points Given is the epression (4-) of a logical function F. F ( y,y )= y y + y y (4-) Problem Statement Demonstrate an ability to:. apply the algebraic manipulation metho to erive the minimum number of literals sum of proucts (SOP) representation of a logic/switching function F. Hint # For full creit, give answers to all questions, prepare all require circuit iagrams, write all equations for which the space has been reserve, an show all symbolic an numerical epressions whose evaluation prouces shown numerical results. Problem Solution For full creit, eplicit emonstration of unerstaning the following solution steps is epecte. 4. Using the algebraic manipulation metho, erive from the epression (4-) the minimum number of literals SOP (sum of proucts) representation of the logical function (4-). Show your manipulation below, or on the opposite page, an enter the results in the space reserve for equation (4-). F = y y + y y = = y y y y = = (y +y )(y +y ) = = y y +y y = y y Representation of F to be grae: F = y y. +y y (4-) //7

Digital Logic Design. Midterm #1

Digital Logic Design. Midterm #1 The University of Toleo s7ms_il7.fm - EECS: igital Logic esign r. nthony. Johnson Stuent Name_ igital Logic esign Miterm # Problems Points. 3. 4 3. 6 4. Total 5 Was the eam fair? yes no /6/7 The University