2. 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
3. FIRST OF ALL WE DISCUSS
EXCLUSIVE GATE
• XOR Symbol
S= A B
A
B
Sum
+
4. 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 B
C S
A•B A B
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0
+
5. 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+
+
7. 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.
12. 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
13. 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
14. 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.
15. 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.
16. 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
17. 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
18. 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
19. 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
20. 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
