PRESENTATION HALF&FULL ADDER

Present by: MUHAMMAD YASIR

WHAT IS ADDER

• In electronics an adder is digital circuit that perform addition of numbers. In modern computer adder reside in the arithmetic logic unit (ALU).

• Adders are important not only in the computer but also in many types of digital systems in which the numeric data are processed.

Types of adder:

• Half adder

• Full adder

FIRST OF ALL WE DISCUSS EXCLUSIVE GATE

• XOR Symbol

S= A B

A

B

Sum

+

WRITING THE TRUTH TABLE

• S is the sum

• C is the carry

• If the input is same then XOR is 0

• If the input is Different Then XOR is 1

INPUTS OUTPUTS

A BC S

A•B A B

0 0 0 0

0 1 0 1

1 0 0 1

1 1 1 0

+

WHAT IS HALF ADDER

: The half adder accepts two binary digits on its inputs and produce two binary digits outputs, a sum bit and a carry bit.

The half adder is an example of a simple, functional digital circuit built from two logic gates. The half adder adds to one-bit binary numbers (AB). The output is the sum of the two bits (S) and the carry (C).

• Sum = AB’+A’B or A. B

• Carry=A*B.

• Cout =A + B+AB+

+

DIAGRAM OF HALF ADDER

• Circuit Diagram

A

B

SSUM

CCARRY

WHAT IS FULL ADDER

• The full adder accepts two inputs bits and an input carry and generates a sum output and an output carry.

• The full-adder circuit adds three one-bit binary numbers (Cin, A ,B) and outputs two one-bit binary numbers, a sum (S) and a carry (Cout). The full-adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. binary numbers.

CIRCUIT DIAGRAM FOR FULL ADDER

• A

B

SSUM

CCARRY

CIN

TRUTH TABLE FOR FULL ADDER

• Three input

A,B,Ccarry

Two output

C0ut,Sum

FULL ADDER

• The full adder is usually drawn in a shorthand notation:

FULLADDER

A

B

CIN

CCARRY

SSUM

PARALLEL FULL ADDERS

•Two types of parallel adders w.r.t handling carry.

1. Ripple Carry adder(RCA

2. Look Ahead Carry adder(LACA

RIPPLE CARRY ADDER

• The parallel adder in which previous stage carry output is connected to the next stage carry input

A4

C in2

C out1

C in1

B4 A3 B3 A2 B2 A1 B1

S4 S3 S2 S1

C in4

C out3

C in3

C out2

CARRY PROPAGATION DELAY

• The time difference between the application of input carry to the occurrence of output carry in any stage called Carry propagation delay

SHORTCOMINGS

• Very slow as the carry has to propagate from initial stage to final stage for final sum.

• Final stage sum and final carry out depends upon the calculations done by the all previous stages.

• Sum calculations for large numbers can delay the calculation for enormous amount of time.

LOOK AHEAD CARRY AND RIPPLE CARRY ADDER(TWO IN ONE)

IC 74LS283 is a 4 bit adder with look ahead carry built in features. i.e have extra logic for LAC inside it.

.When we construct 8 bit or 16 bits or 32 bit or 64 bit adders using more than one 74LS283.

We use in these adders ripple carry feature externally and LAC feature internally.

LOOK AHEAD CARRY ADDER

• Carry for each stage is pre calculated with the help of extra hardware/logic circuits to speed up the addition.

• As we know

• C out = ab + (a ⊕ b) C in

• Carry generated =ab=g;

• Carry propagated= a ⊕ b=p so…

• C out = ab + (a ⊕ b) C in= g + p C in

CARRY OUT CALCULATIONS FOR 4 BIT LAC ADDER

• C out1= g1 +p1C in1 (equation 1)………FA#1

• C in2= C out1. ………………………………….FA#2

• C out2= g2 +p2 C in2

• C out2= g2 +p2 C out1.

• C out2=g2 +p2 (g1 +p1 C in1)…… from eq1.

• C out2= g2 +p2g1+p2 p1 C in1…..eq2

• C in3 =C out2………………………………eq3….FA#3

• C out3= g3+p3 C in3

CARRY OUT CALCULATIONS FOR 4 BIT LAC ADDER

• C out3 =g3+p3 C out2…….using eq3

• C out3= g3+p3(g2 +p2g1+p2 p1 C in1)…. Using equ2

• C out3= g3 +p3g2+p3p2g1+p3p2p1 C in 1….. eq4

• C in4= C out3………………… eq5…………………….FA#4

• C out4= g4+p4 C in4

C out4= g4+p4 C out3…… from eq5

C out4=g4+p4(g3 +p3g2+p3p2g1+p3p2p1 C in 1)

C out4= g4+ p4g3 +p4p3g2+p4p3p2g1+p4p3p2p1 C in 1

DRAW LOGIC CIRCUIT DIAGRAM FOR LAC LOGIC

• Inputs …..g1,g2,g3,g4,p1,p2,p3,p4, C in1

• Outputs……C out1,C out2,C out3,Cout4

FULL ADDER WITH LAC LOGIC

•

A1

B1

C in1

C out3

C out2

C out1

C in1

C out4C out4

p2

p3

p4

S4

S3

S2

S1

g2

p2

g3

p3

g4

p4

g1

p1

A3

p1

THEEND