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Figure P1347
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1348 One method of ensuring reliability in data
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transmission systems is to transmit a parity bit along with every nibble, byte, or word of binary data transmitted The parity bit con rms whether an even or odd number of 1 s were transmitted in the data In even-parity systems, the parity bit is set to 1 when the number of 1 s in the transmitted data is odd Odd-parity systems set the parity bit to 1 when the number of 1 s in the transmitted data is even Assume that a parity-bit is transmitted for every nibble of data Design a logic circuit that checks the nibble of data and transmits the proper parity bit for both even- and odd-parity systems
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1344 Design a circuit with a four-bit input representing
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the binary number A3 A2 A1 A0 The output should be 1 if the input value is divisible by 3 Assume that the circuit is to be used only for the digits 0 through 9 (thus, values for 10 to 15 can be don t cares) a Draw the Karnaugh map and truth table for the function b Determine the minimum expression for the function c Draw the circuit, using only AND, OR, and NOT gates
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1349 Assume that a parity bit is transmitted for every
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nibble of data Design two logic circuits that check a nibble of data and its parity bit to determine if there may have been an data transmission error First assume an even-parity system, then an odd-parity system
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1345 Find the simpli ed sum-of-products
representation of the function from the Karnaugh map shown in Figure P1345 Note that x is the don t care term
AB CD 00 01 11 10
1350 Design a logic circuit that takes a 4-bit Gray code
input from an optical encoder and translates it into two 4-bit nibbles of BCD code
1351 Design a logic circuit that takes a 4-bit Gray code
input from an optical encoder and determines if the input value is a multiple of 3
00 0 1 0 0
01 1 1 x 0
11 0 0 1 1
10 0 0 0 0
1352 The 4221 code is a base 10 oriented code that
assigns the weights 4221 to each of 4 bits in a nibble of data Design a logic circuit that takes a BCD nibble as input and converts it to its 4221 equivalent The logic circuit should also report an error in the BCD input if its value exceeds 1001
1353 The 4-bit digital output of each of two sensors
Figure P1345
along an assembly line conveyor belt is proportional to the number of parts which pass by on the conveyor belt in a 30-second period Design a logic circuit that reports an error if the outputs of the two sensors differ by more than one part per 30-second period
1346 Can the circuit for Problem 1340 be simpli ed if
it is known that the input represents a BCD (binary-coded decimal) number, ie, it can never be greater than 1010 If not, explain why not Otherwise, design the simpli ed circuit
Section 4: Logic Modules 1354
a Fill in the Karnaugh map for the logic function de ned by the truth table of Figure P1354 b What is the minimum expression for the function c Realize the function using a 1-of-8 multiplexer
1347 Find the simpli ed sum-of-products
representation of the function from the Karnaugh map shown in Figure P1347
Part II
Electronics
A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
f(A,B,C,D) 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1
1357 Show that the circuit given in Figure P1357
converts 4-bit binary numbers to 4-bit Gray code
G3 B3 4 bit binary code in
B1 B0
Figure P1354
Figure P1357
a Fill in the truth table for the multiplexer circuit shown in Figure P1355 b What binary function is performed by these multiplexers
1358 Suppose one of your classmates claims that the
following Boolean expressions represent the conversion from 4-bit Gray code to 4-bit binary numbers: B3 = G 3 B2 = G 3 G 2 B1 = G 3 G 2 G 1 B0 = G3 G2 G1 G0 a Show that your classmate s claim is correct b Draw the circuit which implements the conversion
S 0 1 1 0 I0 I1 I2 I3 0 0 0 1 I0 I1 I2 I3
x 0 0 1 1
y 0 1 0 1
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