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108Y
16713
ISTM 214 Homework 1
Due day: 9/25
1. (24%) Perform the following number-system conversions
(a) (4310)5 = ( ? )10 = ( ? )2
(b) (10110.0101)2 = ( ? )10 = ( ? )8
(c) (125)10 = ( ? )2 = ( ? )16
(d) (255.55)10 = ( ? )2 = ( ? )8
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2. (16%) Determine the base of the numbers in each case for the following operations
to be correct:
a 4118 4 8 1 8 33 3 8 3 1118 13
(a) 41 / 3 = 13
63
(b) 23 + 44 + 14 + 32 = 223
13 24 9 17
b 2rt3t4rt4tlrt4t3rtz 2r42rt3
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3. (20%) Simplify the following Boolean expressions to a minimum number of literals:
(a) (x + y)’(x’ + y’)
(b) w’x(z’ + y’z) + x(w + w’yz)
x yyalx'ty
x'x'y x'y'y
Wxztw'xy'ztwxtw'xyz
Wxzly'tytwxztwx
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4. (20%) List the truth table of the function:
三
xiitxgix拼
(a) F = xy + xy’ + y’z
(b) F = ac + b’c’
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5. (20%) Draw logic diagrams of the circuits that implement the functions in Problem 4.
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