Page 79 - Computer science 868 Class 12
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0 1 0 0 0 1 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 0 1 0 0
1 1 0 0 0 0 0 0 0 1 0
1 1 1 0 0 0 0 0 0 0 1
From the truth table we can see that:
D = A '.A '.A '
0
2
0
1
D = A '.A '.A 0
1
2
1
D = A '.A .A ' A 2 A 1 A 0
2
0
2
1
D = A '.A .A 0
3
1
2
D = A .A '.A ' 0
1
4
2
D = A .A '.A 0 D 0
5
1
2
D = A .A .A ' D 1
0
2
1
6
D = A .A .A 0
2
1
7
To draw the logic circuit diagram of a 3 to 8 decoder, all three input D 2
variables are connected both directly and through the NOT gate to get
the complemented input. The input variables are connected to eight AND D 3
gates. Only one AND gate produces High output(1) for a particular input
combination and represents the corresponding Octal number, while the D 4
other AND gates are 0.
The logic circuit diagram is as shown. D 5
Working Principle of Binary to Octal Decoder:
D
If we take A = 1 A = 1 and A = 0 as input the output across the eight gates 6
1
2
0
is as follows: D 7
D = A '.A '.A ' i.e., 0.0.1 = 0
1
0
2
0
D = A '.A '.A i.e., 0.0.0 = 0
0
1
1
2
D = A '.A .A ' i.e., 0.1.1 = 0
1
2
0
2
D = A '.A .A i.e., 0.1.0 = 0
0
2
1
3
D = A .A '.A ' i.e., 1.0.1 = 0
1
2
0
4
D = A .A '.A i.e., 1.0.0 = 0
0
1
2
5
D = A .A .A ' i.e., 1.1.1 = 1
1
0
2
6
D = A .A .A i.e., 1.1.0 = 0
2
0
7
1
We conclude output is 1 only across AND gate D which represents octal value 6.
6
2.5.2 Binary to Decimal Decoder
A Decimal number is represented using four bits. A Binary to Decimal Decoder has four input lines and 10 output lines
to represent digits from 0 to 9.
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Computer Hardware 77

