3. Combinational Circuits
Combinational Logic Circuits
are memory less digital logic
circuits whose output at any
instant in time depends only on
the combination of its inputs.
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5. 5
Half Adder
• The half adder adds two single binary input digits A and B.
• It has two outputs, sum (S) and carry (C).
• The carry signal represents an overflow into the next digit of a multi-digit
addition.
Inputs Outputs
A B Carry Sum
0 0 0 0
1 0 0 1
0 1 0 1
1 1 1 0
6. 6
Half Adder
Inputs Outputs
A B Carry Sum
0 0 0 0
1 0 0 1
0 1 0 1
1 1 1 0
Schematic of Half adder
Logic Circuit of Half adder
7. 7
Full Adder
• A full-adder is a combinational circuit that forms the
arithmetic sum of three input bits
• It consists of 3 inputs and 2 outputs
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n-bit adder/Parallel Adder
•Cascade n full adder (FA) blocks to form a n-bit adder.
•Carries propagate or ripple through this cascade, n-bit ripple carry adder.
Carry-in c0 into the LSB position provides a convenient way to
perform subtraction.
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n-bit subtractor/Parallel subtractor
•Recall A – B is equivalent to adding 2’s complement of B to A.
•2’s complement is equivalent to 1’s complement + 1.
•A – B = A + B + 1
•2’s complement of positive and negative numbers is computed similarly.
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Parallel Adder/Subtractor
Addition and Subtraction operations can be combined into one circuit with one common binary
adder. This is done by including an exclusive-OR gate with each full adder.
M=0 Circuit acts as Adder
M=1 Circuit acts as Subtractor
M=0 B 0 = B
M=1 B 1 = B
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Drawback
• Sum and carry of any stage cannot be produced until the input carry occurs.
• This leads to a time delay in addition process.
• This delay is known as Carry Propagation Delay.
• One method of speeding up this process by eliminating inter stage carry delay is
called lookahead-carry addition
