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00 01 01 10
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Full-Adder
By contrast, a full adder has three binary inputs (A, B, and Carry in) and two binary outputs (Carry out and Sum). The truth table summarizes the operation.
Digital Fundamentals
Tenth Edition
Floyd
Chapter 6
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education©, U2p0p0e8rPSeaadrdsolenREidvuecr,aNtioJn07458. All Rights Reserved
Cout S
00 01 01 10 01 10 10 11
S AS B Cin Cout
Symbol
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
10 1 0 1 1
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Half-Adder
Basic rules of binary addition are performed by a half adder, which has two binary inputs (A and B) and two binary outputs (Carry out and Sum).
Quiz 2 (20 minutes)
Refer to Karnaugh map :
1. Write the standard SOP (Sum of
CD
Product) form for the output (5 AB
00 01 11 10
points)
2. Write the standard POS (product 00 1 0 1 1
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Parallel Adders
Full adders are combined into parallel adders that can add binary numbers with multiple bits. A 4-bit adder is shown.
of Sum) form for the output (5
points)
01 1 1 0 1
3. Write the minimum SOP form. Draw the circuit. (10 points)
11 0 0 x 1
4. Write the minimum POS form. Draw the circuit (10 points)
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Full-Adder Notice that the result from the previous example can be read directly on the truth table for a full adder.
SummaΒιβλιοθήκη Baiduy
Full-Adder
1
S A
S
1
AS S 0
Sum
0
B Cout 0
B Cout 1
For the given inputs, determine 1 the intermediate and final outputs
Cout
1
of the full adder.
The first half-adder has inputs of 1 and 0; therefore the Sum =1 and the Carry out = 0.
A full-adder can be constructed from two half adders as shown:
A AS S
AS S
Sum
B
B Cout
Cin
B Cout
Cout
Inputs
A B Cin
00 0 00 1 01 0 01 1 100 101 110 111
Outputs
The second half-adder has inputs of 1 and 1; therefore the Sum = 0 and the Carry out = 1.
The OR gate has inputs of 1 and 0, therefore the final carry out = 1.
Inputs
A B Cin
00 0 00 1 01 0 01 1 100 101 110 111
Outputs
Cout S
00 01 01 10 01 10 10 11
1
S A
S
1
AS S 0
0
B Cout 0
B Cout 1
1
Sum
Cout 1
Floyd, Digital Fundamentals, 10th ed
The inputs and outputs can be summarized on a truth table.
The logic symbol and equivalent circuit are:
AS S
S
A
B Cout
B
Cout
Inputs Outputs
AB
00 01 10 11
Cout S
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Full-Adder
By contrast, a full adder has three binary inputs (A, B, and Carry in) and two binary outputs (Carry out and Sum). The truth table summarizes the operation.
Digital Fundamentals
Tenth Edition
Floyd
Chapter 6
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education©, U2p0p0e8rPSeaadrdsolenREidvuecr,aNtioJn07458. All Rights Reserved
Cout S
00 01 01 10 01 10 10 11
S AS B Cin Cout
Symbol
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
10 1 0 1 1
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Half-Adder
Basic rules of binary addition are performed by a half adder, which has two binary inputs (A and B) and two binary outputs (Carry out and Sum).
Quiz 2 (20 minutes)
Refer to Karnaugh map :
1. Write the standard SOP (Sum of
CD
Product) form for the output (5 AB
00 01 11 10
points)
2. Write the standard POS (product 00 1 0 1 1
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Parallel Adders
Full adders are combined into parallel adders that can add binary numbers with multiple bits. A 4-bit adder is shown.
of Sum) form for the output (5
points)
01 1 1 0 1
3. Write the minimum SOP form. Draw the circuit. (10 points)
11 0 0 x 1
4. Write the minimum POS form. Draw the circuit (10 points)
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Full-Adder Notice that the result from the previous example can be read directly on the truth table for a full adder.
SummaΒιβλιοθήκη Baiduy
Full-Adder
1
S A
S
1
AS S 0
Sum
0
B Cout 0
B Cout 1
For the given inputs, determine 1 the intermediate and final outputs
Cout
1
of the full adder.
The first half-adder has inputs of 1 and 0; therefore the Sum =1 and the Carry out = 0.
A full-adder can be constructed from two half adders as shown:
A AS S
AS S
Sum
B
B Cout
Cin
B Cout
Cout
Inputs
A B Cin
00 0 00 1 01 0 01 1 100 101 110 111
Outputs
The second half-adder has inputs of 1 and 1; therefore the Sum = 0 and the Carry out = 1.
The OR gate has inputs of 1 and 0, therefore the final carry out = 1.
Inputs
A B Cin
00 0 00 1 01 0 01 1 100 101 110 111
Outputs
Cout S
00 01 01 10 01 10 10 11
1
S A
S
1
AS S 0
0
B Cout 0
B Cout 1
1
Sum
Cout 1
Floyd, Digital Fundamentals, 10th ed
The inputs and outputs can be summarized on a truth table.
The logic symbol and equivalent circuit are:
AS S
S
A
B Cout
B
Cout
Inputs Outputs
AB
00 01 10 11
Cout S