zzanswer for january 2012-inb10403
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ANSWER FOR JANUARY 2012 DIGITAL SYSTEMS
SECTION A
Question 1:
(a) What is decimal value represented if the number is stored as BCD 8421, BCD 5421 and BCD
excess 4?
i. 1000 0111
BCD 8421 1000 0111
Decimal 8 7 BCD 5421 1000 0111
Decimal 5 7 BCD excess 4 1000 0111
Decimal 3 2
ii. 0011 0100
BCD 8421 0011 0100
Decimal 3 4 BCD 5421 0011 0100
Decimal 3 4 BCD excess 4 0011 0100
Decimal 0 1
iii. 1100 1001
BCD 8421 1100 1001
Decimal 8 7 BCD 5421 1100 1001
Decimal 5 7 BCD excess 4 1100 1001
Decimal 4 3
(b) Express ‘UniKL’ in ASCII-7 by using even parity and insert the data in gray code based
microcontroller.
WORD U n i K L ASCII-7 1010101 1101110 1101001 1001011 1001100
Even Parity 01010101 01101110 01101001 01001011 01001100
Gray Code
Question 2:
(a) Circuit Diagram,
i. Write function (F) of the circuit.
Gate 1: A’
Gate 2: A’ + B
Gate 3: (A’ + B)’ = A’’ + B’
Gate 4: (A’ + B)’ . B = A’’B + B’B
Gate 5: ((A’ + B)’ . B)’ = A’’’ B’ + B’’B’
Gate 6: ((A’ + B)’ . B)’ . C = A’’’B’C + B’’B’C
Gate 7: (((A’ + B)’ . B)’ . C) + B = A’’’B’C + B’’B’C + B
The answer is,
F = (((A’ + B)’ . B)’ . C) + B
A B
C F
ii. Calculate Minterm of F:
Truth Table
A B C F
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
F = A’B’C + A’BC’ + A’BC + AB’C + ABC’ + ABC
iii. Minimize circuit by using Karnaugh Maps (K-Maps):
*Group of 4 minterms of K-Maps,
F = A’B’C + AB’C + A’BC + ABC
F = (A’ + A) B’C + (A’ + A) BC
F = (1) B’C + (1) BC
F = B’C + BC
F = (B’ + B) C
F = (1) C
F = C
*Group of 2 minterms of K-Maps.
F = A’BC’ + ABC’
F = (A’ + A) BC’
F = (1) BC’
F = BC’
**The minimized function of F is BC’ + C.
0
0
1
1
0
1
00 01 BC
A
1
1
11
1
1
10
iv. Draw the minimize circuit:
Question 3:
Calculate the following by using 2’s Complement. Convert the decimal value into binary first. Justify
your answer by converting 2’s Complement result in decimal.
i. -10 -7
1010 = 10102
1010 – Binary (1010)
0101 – 1’s Complement (-1010)
1
0110 – 2’s Complement
710 = 01112
0111 – Binary (710)
1000 – 1’s Complement (-710)
1
1001 – 2’s Complement
ii. -3 -5
310 = 00112
0011 – Binary (310)
1100 – 1’s Complement (-310)
1
1101 – 2’s Complement
510 = 01012
0101 – Binary (510)
1010 – 1’s Complement (-510)
1
1011 – 2’s Complement
B
C F
iii. -47 -3
4710 = 2F16 = 00111112
Pad to 8-bits binary of 00111112 = 000111112
00011111 – Binary (2F16)
11100000 – 1’s Complement (-2F16)
1
11100001 – 2’s Complement
310 = 00112
0011 – Binary (310)
1100 – 1’s Complement (-310)
1
1101 – 2’s Complement
iv. -14 -10
1410 = 11102
1110 – Binary (1410)
0001 – 1’s Complement (-1410)
1
0010 – 2’s Complement
1010 = 10102
1010 – Binary (1010)
0101 – 1’s Complement (-1010)
1
0110 – 2’s Complement
Question 4:
The following English expression describes the way a logic circuit needs to operate in order
to drive a seatbelt warning indicator in a car.
“If the driver is present and the driver is not buckled up and the ignition
switch is on. Then turn on the warning light.”
Describe the circuit using Boolean algebra, schematic diagram with logic symbols, truth table
and the timing diagram.
**The answer still in,
K.I.V