Digital Logic Design. Midterm #1

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1 The University of Toleo f6ms_il7.fm - EECS: igital Logic esign r. Anthony. Johnson Stuent Name_ igital Logic esign Miterm # Problems Points Total 5 Was the eam fair? yes no 9/9/6

2 The University of Toleo f6ms_il7.fm - EECS: igital Logic esign r. Anthony. Johnson 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 Switching Function F(A,B). Given net to the truth table is a list of boolean function names. For the names in the list, inicate which names are, an which names are not, the name of the function F(A,B). a b c F(a,b,c) yes no not applicable AN, XNOR, NAN, NOR..3 POS (prouct of sums) representation of Switching Functions lens itself to irect implementation using the following types of two-level logic circuits: yes no not applicable NOR-NOR AN-NAN NAN-NAN OR-AN 9/9/6

3 The University of Toleo f6ms_il7.fm - 3 EECS: igital Logic esign r. Anthony. Johnson Stuent Name_ Problem 4 points Positional representations of the functions (i), i=,,3, in various raies are shown in Table. i function (i) (i) 3 3 (i) s ecimal representation 3-3 Table eight-bit base-two representation of (i) -(i) 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 ivision 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. Show your computation on the opposite page, an enter the results into Table. Hint#:irect 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 process, an the result of the process of ivision of (3) by (). Show your calculation of the quotient an the remainer in the space reserve for equations (-.) ivisor Result of calculations uner. to be grae Quotient ivien Remainer (-) Quotient: _ Remainer: 9/9/6

4 The University of Toleo f6ms_il7.fm - 4 EECS: igital Logic esign r. Anthony. Johnson Stuent Name_ Problem 3 6 points Equation (3-) shows an incompletely specifie logical/switching function F (A,B,C,) in the ecimal lists of sums-of, minterms an on t cares, representation. F (A,B,C,) = Σ(, 3, 5, 7, 9, 5) +(A,B,C,) = Σ(4, 6,, 3) (3-) Problem Statement On the eample of the given logic function F emonstrate 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 epression of F, 3. apply e Morgan s theorem to erive a minimal number of literals epression of F, 4. esign the two-level NAN-NAN implementation of the SOP form of function F, an the two-level NOR-NOR implementation of the POS form of function F, as specifie uner 3.4 an 3.5 below. Hint # For full creit, give answers to all questions, prepare all require circuit iagrams, write all equations for which the space is reserve, an show all algebraic an numerical epressions whose evaluation prouces shown results. Problem Solution An eplicit emonstration of unerstaning the following solution steps is epecte. 3. In the space reserve for Figure 3-(a), prepare the Truth table representation of the function F. A B C F (a) C AB (b) F = A + B +C Figure 3- Representation forms of the function F. (a)karnaugh map. (b)minimum number of literals SOP representation of F. (c)minimum number of literals POS representation of F. (c) F = (A + ) (B + ) (C + ) () 9/9/6

5 The University of Toleo f6ms_il7.fm - 5 EECS: igital Logic esign r. Anthony. Johnson Stuent Name_ 3. In the space reserve for Figure 3-(b), prepare the Karnaugh map representation of the function F. 3.3 Apply the Karnaugh map minimization metho to erive the minimum number of literals SOP (sum-of-proucts) representation of the function F. Enter the erive algebraic epression in the space reserve for Figure 3-(b). 3.4 Apply e Morgan s theorem to erive the minimum number of literals POS (prouct-of-sums) representation of the function F. Enter the erive algebraic epression in the space reserve for Figure -(c). 3.5 In the space reserve for Figure 3-(a), prepare a logic circuit iagram of the two-level NAN-NAN form of implementation of the erive minimum number of literals SOP epression of the function F. 3.6 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 minimum number of literals POS epression of the function F. A A B F B F C C (a) (b) Figure 3- Two-level implementation of the minimum number of literals epressions of the functions F an F. (a)nan-nan implementation of F. (b)nor-nor implementation of F. 9/9/6

6 The University of Toleo f6ms_il7.fm - 6 EECS: igital Logic esign r. Anthony. Johnson Stuent Name_ Problem 4 points Given is the epression (4-) of a logical function F. F (X,Y,Z) = X Y Z + X Y Z + X Y Z + X Y Z (4-) Problem Statement emonstrate 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 logic function (4-). Show your manipulation below, or on the opposite page, an enter the results in the space reserve for equation (4-). F = X Y Z + X Y Z + X Y Z + X Y Z = = (X Z + X Z) Y + (X Z + X Z) Y = = (X Z + X Z) (Y+ Y) = (X Z + X Z) = = X Z + X Z Representation of F to be grae: F = X Z + X Z (4-) 9/9/6

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