Digital System Design
Lecture - 3.1
Decoder
• A combinational circuit that converts binary information from n input
lines to a maximum of 2n unique output lines
• Called n-to-m line decoders where m<=2n
• Purpose is to generate the 2n (or less) minterms of n input variables
• Application: Binary to Octal Conversion (Input variables represent a
binary number, and output represents eight digits in the octal number
system)
• A 3-to-8 line decoder can be used to decode any 3-bit code to provide
8-outputs
• Example: 3:8, 2:4, 4:16 Decoder
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3-to-8 Decoder
Truth Table:
Block Diagram:
X
Y
Z
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3-to-8 Decoder (Contd.)
Circuit Diagram:
Practice Work:
Design a BCD-to-decimal
decoder with the help of
don’t care conditions.
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Implementation Using Decoder
Input Output
x y z S C
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
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Implementation Using Decoder (Contd.)
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Encoder
• A combinational circuit that performs the reverse operation of
Decoder
• It encodes 2n input lines to n output lines
• Produces a binary code equivalent to the input
• Called m-to-n line encoders where m=2n
• Only one of the inputs become "high" (logic state "1") at a time.
• Application: Octal to Binary Conversion
• Example: 4:2, 8:3, 16:4 Encoder
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8-to-3 Encoder
Truth Table:
Block Diagram:
X
Y
Z
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8-to-3 Encoder (Contd.)
Circuit Diagram:
Practice Work:
Design a
Decimal-to-BCD
Encoder.
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Priority Encoder
• Encoder with priority function
• Multiple inputs may be true simultaneously
• Higher priority input gets the precedence
• Even if more than one input is ‘1’ at the same time, the output will be
the (binary) code corresponding to the input, which is having higher
priority
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Priority Encoder
Priority
(high to
low)
Y0
Y1
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Practice Problems
I. A combinational circuit is specified by the following three Boolean functions:
F1 (A, B, C) = Σ(2, 4, 7)
F2 (A, B, C) = Σ(0, 3)
F3 (A, B, C) = Σ(0, 2, 3, 4, 7)
Implement the circuit with a decoder constructed with NAND/AND gates. Minimize the
number of inputs in the external gates.
II. Implement a full adder with a decoder and NAND gates.
III. Design a combinational circuit that compares two 4-bit numbers to check if they are equal.
The circuit output is equal to 1 if two numbers are equal and 0 otherwise. Mention the
equation of the circuit.
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