kogge stone adder
DESCRIPTION
TRANSCRIPT
Kogge Stone adder
Peeyush Pashine(2011H140033H)
Prefix adder
• What is a prefix circuit ?
CSE 246 3
Prefix Adder
• Given:– n inputs (gi, pi)– An operation o
• Compute:– yi= (gi, pi) o … o (g1, p1) ( 1 <= i <= n)
• Associativity– (A o B) o C = A o ( B o C)
(g’’, p’’) o (g’, p’) = (g, p) g=g’’ + p’’g’ p=p’’p’
gi=
pi=
a, i=1
aibi , otherwise
1, i=1
ai xor bi , otherwise
Group PG logic
CSE 246 5
Prefix Adder: Graph Representation
• Example: Ripple Carry Adder
ai bi
(gi , pi)
x y
xoy xoy
Prefix adder(continued…)
Prefix circuit theory provides a solid theoretical basis for wide range of design trade-offs between
• Delay• Area• Wire complexity
Basic type of prefix circuits
8CSE 246
Prefix Adders: Brent – Kung Adder15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
sc(16) = 26 dc(16) = 6 total = 32
Kogge stone adder radix 2(A
0, B
0)
(A1, B
1)
(A2, B
2)
(A3, B
3)
(A4, B
4)
(A5, B
5)
(A6, B
6)
(A7, B
7)
(A8, B
8)
(A9, B
9)
(A10
, B10
)
(A11
, B11
)
(A12
, B12
)
(A13
, B13
)
(A14
, B14
)
(A15
, B15
)
S0
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
Kogge Stone adder
Brent –kung adder
11CSE 246
Kogge stone Prefix Adder
8 7 6 5 4 3 2 1
35
36
7
10
9
14
11
15
13
22 18
15
21
26
2836
12CSE 246
Prefix Adders: Conditional Sum Adder
• For output yi, there is an alphabetical tree covering inputs (xi, xi-1, …, x1)
8 7 6 5 4 3 2 1 alphabetical
tree: Binary tree Edges do not
cross
13CSE 246
Prefix Adders: Conditional Sum Adder
• From input x1, there is a tree covering all outputs (yi, yi-1, …, y1)
8 7 6 5 4 3 2 1
The nodes in this tree can be reduced to
(g, p) o c = g+pc
Kogge stone radix 4 adder(a
0, b
0)
(a1, b
1)
(a2, b
2)
(a3, b
3)
(a4, b
4)
(a5, b
5)
(a6, b
6)
(a7, b
7)
(a8, b
8)
(a9, b
9)
(a1
0, b
10)
(a1
1, b
11)
(a1
2, b
12)
(a1
3, b
13)
(a1
4, b
14)
(a1
5, b
15)
S0
S1
S2
S3
S4
S5
S6
S7
S8
S9
S1
0
S1
1
S1
2
S1
3
S1
4
S1
5
Comparison between radix 2 and radix 4 koggstone