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1330 How many address inputs do you need if the number of words in a memory array is 16
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Digital logic circuits are at the basis of digital computers Such circuits operate strictly on binary signals according to the laws of Boolean algebra Combinational logic circuits can implement arbitrary Boolean logic functions Combinational logic circuits include all of the logic gates AND, OR, NAND, NOT, and XOR as well as logic modules such as multiplexers and read-only memory
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CYU 131 CYU 132 CYU 133 CYU 134 CYU 135 CYU 136 CYU 137 CYU 138 CYU 1316 CYU 1317 CYU 1318 CYU 1320 CYU 1322 CYU 1323 CYU 1324 CYU 1325 CYU 1326 (a) 100111; (b) 111011; (c) 100000000; (d) 0011100; (e) 011001; (f) 0110011; (g) 10000000011; (h) 100000011001; (i) 100000000000011101 (a) 13; (b) 27; (c) 23; (d) 06875; (e) 0203125; (f) 02128906 02128906255; (g) 596875; (h) 91203125; (i) 22340820312 (a) 207510 ; (b) 7410 ; (c) 1510 ; (d) 2110 ; (e) 1000002 ; (f) 10000002 ; (g) 110010112 ; (h) 100011111112 4,096 39 mV (a) 111110000011; (b) 00111001001; (c) 10100110; (d) 1AE; (e) B9; (f) 6ED (a) 00010111; (b) 01101001; (c) 0100010 (a) 0000 1011 1101; (b) 1101 0100 0111; (c) 0101 1010 W Z+X Z Y Z+X Z Nine gates No f =a b c d +a c d +a b c+b c d f =a b+a c f =a b+a b+c f =a b c d +a b c d +a b c d +a b c d f =a b c d +b c d +a d +b c d +a c
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CYU 1327 CYU 1328 CYU 1329 CYU 1330
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I1 I0 = 11 For the rst part, use the same method as in Check Your Understanding Exercise 1327, but for an 8-to-1 MUX For the second part, I2 I1 I0 = 101 I2 I1 I0 = 100 4
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HOMEWORK PROBLEMS
Section 1: Number Systems 131 Convert the following base 10 numbers to hex and
binary: a 401 b 273 binary: a A b 66 a 27125 c 15 d 38 e 56
1312 Using the method of proof by perfect induction,
show that (X + Y ) (X + X Y ) = Y
132 Convert the following hex numbers to base 10 and
c 47 b 53375 d 21 e 13 d 5427
1313 Using De Morgan s theorems and the rules of
Boolean algebra, simplify the following logic function: F (X, Y, Z) = X Y Z + X Y Z + X (Y + Z)
133 Convert the following base 10 numbers to binary:
c 3732
1314 Simplify the expression
f (A, B, C, D) = ABC + ACD + BCD
134 Convert the following binary numbers to hex and
base 10: a 1111 b 1001101 e 11101 f 101000 c 1100101 d 1011100
1315 Simplify the logic function
F (A, B, C) = A B C + A B C + A B C + A B C using Boolean algebra
135 Perform the following additions all in the binary
system: a 11001011 + 101111 b 10011001 + 1111011 c 11101001 + 10011011
1316 Find the logic function de ned by the truth table
given in Figure P1316
A 0 0 0 0 1 1 1 1
B 0 0 1 1 0 0 1 1
C 0 1 0 1 0 1 0 1
F 0 1 0 1 1 1 1 1
136 Perform the following subtractions all in the binary
system: a 10001011 1101111 b 10101001 111011 c 11000011 10111011
137 Assuming that the most signi cant bit is the sign
bit, nd the decimal value of the following sign-magnitude form eight-bit binary numbers: a 11111000 b 10011111 c 01111001
Figure P1316
1317 Determine the Boolean function describing the
operation of the circuit shown in Figure P1317
138 Find the sign-magnitude form binary
representation of the following decimal numbers: a 126 b 126 c 108 d 98
139 Find the two s complement of the following binary
numbers: a 1111 b 1001101 c 1011100 d 11101
C D F
Section 2: Combinational Logic 1310 Use a truth table to prove that B = AB + AB 1311 Use truth tables to prove that
BC + BC + BA = A + B
Figure P1317
Part II
Electronics
1318 Use a truth table to show when the output of the
circuit of Figure P1318 is 1
x3 x2 x1
ignition key is turned and either a door is open or a seat belt is not fastened The buzzer also sounds when the key is not turned but the lights are on In addition, the car will not start unless the key is in the ignition, the car is in park, and all doors are closed and seat belts fastened Design a logic circuit that takes all of the inputs listed and sounds the buzzer and starts the car when appropriate
Output
1323 An on/off start-up signal governs the compressor
motor of a large commercial air conditioning unit In general, the start-up signal should be on whenever the output of a temperature sensor (S) exceeds a reference temperature However, you are asked to limit the compressor start-ups to certain hours of the day and also enable service technicians to start up or shut down the compressor through a manual override A time-of-day indicator (D) is available with on/off outputs as is a manual override switch (M) A separate timer (T ) prohibits a compressor start-up within 10 minutes of a previous shutdown Design a logic diagram that incorporates the state of all four devices (S, D, M, and T ) and produces the correct on/off condition for the motor start-up
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