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Computer Platforms - Research Paper Example

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1. Draw out the truth-table for the XOR function. Make this using only NAND gates. Define and use DeMorgan's theorem both in Boolean and diagrammatic terms in the solution. Why is the EXOR function considered useful in binary addition circuits'
As per Mano (2000, p.47), "The generalised form of DeMorgan's theorem states that the complement of a function is obtained by interchanging AND and OR operators and complementing each literal." This can be expressed algebraically as follows:
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Download file to see previous pages A binary input of 0100 would light four LEDs in a row whilst a binary input of 0101 would light five LEDs in a row. Derive the truth-table for a 4 bit input/ 16 bit output decoder which would be used to power this linear display.
Solution: Let x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 and x15 represent the linear array of LEDs. Let A, B, C and D represent the binary input terminals. The truth-table for the linear display is shown in Figure 2.2.
...
Table 2.1 gives details as to which segments should be energised to display various decimal values at the 4-pin input.
Decimal
A
B
C
D
Segments
0
0
0
0
0
a, b, c, d, e, f
1
0
0
0
1
b, c
2
0
0
1
0
a, b, g, e, d
3
0
0
1
1
a, b, c, d, g
4
0
1
0
0
b, c, f, g
5
0
1
0
1
a, c, d, f, g
6
0
1
1
0
c, d, e, f, g
7
0
1
1
1
a, b, c
8
1
0
0
0
a, b, c, d, e, f, g
9
1
0
0
1
a, b, c, f, g
Table 2.1 Truth-table for BCD-to-seven-segment decoder

Hence we can derive expressions for each segment, as follows:
a = A'B'C'D' + A'B'CD' + A'B'CD + A'BC'D + A'BCD + AB'C'D' + AB'C'D
b = A'B'C'D' + A'B'C'D + A'B'CD' + A'B'CD + A'BC'D' + A'BCD + AB'C'D' + AB'C'D
c = A'B'C'D' + A'B'C'D + A'B'CD + A'BC'D' + A'BC'D + A'BCD' + A'BCD + AB'C'D'
+ AB'C'D
d = A'B'C'D' + A'B'CD' + A'B'CD + A'BC'D + A'BCD' + AB'C'D'
e = A'B'C'D' + A'B'CD' + A'BCD' + AB'C'D'
f = A'B'C'D' + A'BC'D' + A'BC'D + A'BCD' + AB'C'D' + AB'C'D
g = A'B'CD' + A'B'CD + A'BC'D' + A'BC'D + A'BCD' + AB'C'D' + AB'C'D

2.b A display composed of a linear array of LEDs, is to respond to a 4-bit binary input which is dependent on the absolute binary value by lighting each successful element. A binary input of 0100 would light four LEDs in a row whilst a binary input of 0101 would light five LEDs in a row. Derive the truth-table for a 4 bit input/ 16 bit output decoder which would be used to power this linear display.
Solution: Let x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 and x15 represent the linear array of LEDs. Let A, B, C and D represent the binary input terminals. The truth-table for the linear display is shown in Figure 2.2.

Table 2.2 Truth-table for LEDs of linear display


3.a The decimal number 101 may be represented in binary as 01100101. Using One's ...Download file to see next pagesRead More
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