Full Adder

Chapter 10

BINARY ARITHMETIC, DECODING AND MUX LOGIC UNITS

Lesson 1

Binary Addition and Subtraction

Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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Outline • • • • •

Half Adder Full Adder Addition of two 4-bit numbers Addition using a MSI IC Subtraction Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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Half adder • Cy'0 —carry bit obtained at an output of adder circuit, • S — sum bit obtained at another output • Circuit is called half adder (H.A.) if A add B = S plus Cy’0


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Half Adder 2 inputs and 2 outputs Inputs A B 0 0 1 1

0 1 0 1

Outputs S Cy’0 0 1 1 0

0 0 0 1


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Half Adder • Circuit Cy’0 S A B Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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Full adder • Cyi–1 and Cyi —carry bits at the input and output of adder circuit at ith place, • S — sum bit obtained at another output • Circuit is called full adder (H.A.) if Cyi–1 add A add B = S plus Cyi' • Place from right most to the leftmost in a number — 0 to n–1 Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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Full Adder 2 inputs and 2 outputs A 0 0 0 0 1 1 1 1

Inputs B Cyi–1

Outputs S Cyi

0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 20051 Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education,

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Full Adder • Circuit Cy’0

A B Cyi–1

S


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4-bit Adder A3 B3 A2 B2 A1 B1 A0 B0 Cy3

Cy2

Cy1

Cy0

Cy-1

F.A

F.A

F.A

F.A

S3

S2

S1

S0


0

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4-bit Adder circuit MSI IC S3 S2 S1 S0 7483

Cyi-1

A3B3A2B2A1B1A0B0 Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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Subtraction • Subtraction of B from A is addition of binary number A and two’s complement of B • Two’s complement of B is addition of 1 with 1’s complement of B. • A method to find 1’s complement of a bit is using an XOR at which one of the input = 1 Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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B3

A3 Cy3

B0

B1

B2 A2 Cy2

A1 Cy1

A0 Cy0

Cy-1

F.A

F.A

F.A

F.A

S3

S2

S1

S0

= 0 for Add = 1 for subtract

4-bit Adder Cum subtractor Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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4-bit Adder/Subtractor circuit MSI IC 7483

S3 S2 S1 S0 Cyi-1

Add/subtract A3B3A2B2A1B1A0B0 Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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Summary


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Addition • Full adder takes two bits in input and outs sum bit and carry bit • Full adder takes carry and two bits in input and outs sum bit and carry bit • XOR gate generates carry • 3-AND- 1-OR array generated Sum Ch10L1-"Microcontrollers....", Raj Kamal, from Pearson Education, 2005

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Subtraction • Second input of full adder is through an XOR • XOR connects other input to Sub/Add control signal and when 1 then full adder implements subtractor.


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End of Lesson 1 on

Binary Addition and Subtraction


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THANK YOU


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