A lookahead carry unit (LCU) is a logical unit in digital circuit design used to decrease calculation time in adder units and used in conjunction with carry look-ahead adders (CLAs).
A single 4-bit CLA is shown below:
By combining four 4-bit CLAs, a 16-bit adder can be created but additional logic is needed in the form of an LCU.
The LCU accepts the group propagate (
P
G
) and group generate (
G
G
) from each of the four CLAs.
P
G
and
G
G
have the following expressions for each CLA adder:
P
G
=
P
3
⋅
P
2
⋅
P
1
⋅
P
0
G
G
=
G
3
+
P
3
⋅
G
2
+
P
3
⋅
P
2
⋅
G
1
+
P
3
⋅
P
2
⋅
P
1
⋅
G
0
The LCU then generates the carry input for each CLA.
Assume that
P
i
is
P
G
and
G
i
is
G
G
from the ith CLA then the output carry bits are
C
4
=
G
0
+
P
0
⋅
C
0
C
8
=
G
4
+
P
4
⋅
C
4
C
12
=
G
8
+
P
8
⋅
C
8
C
16
=
G
12
+
P
12
⋅
C
12
Substituting
C
4
into
C
8
, then
C
8
into
C
12
, then
C
12
into
C
16
yields the expanded equations:
C
4
=
G
0
+
P
0
⋅
C
0
C
8
=
G
4
+
G
0
⋅
P
4
+
C
0
⋅
P
0
⋅
P
4
C
12
=
G
8
+
G
4
⋅
P
8
+
G
0
⋅
P
4
⋅
P
8
+
C
0
⋅
P
0
⋅
P
4
⋅
P
8
C
16
=
G
12
+
G
8
⋅
P
12
+
G
4
⋅
P
8
⋅
P
12
+
G
0
⋅
P
4
⋅
P
8
⋅
P
12
+
C
0
⋅
P
0
⋅
P
4
⋅
P
8
⋅
P
12
C
4
corresponds to the carry input into the second CLA;
C
8
to the third CLA;
C
12
to the fourth CLA; and
C
16
to overflow carry bit.
In addition, the LCU can calculate its own propagate and generate:
P
L
C
U
=
P
0
⋅
P
4
⋅
P
8
⋅
P
12
G
L
C
U
=
G
12
+
G
8
⋅
P
12
+
G
4
⋅
P
8
⋅
P
12
+
G
0
⋅
P
4
⋅
P
8
⋅
P
12
+
C
0
⋅
P
0
⋅
P
4
⋅
P
8
⋅
P
12
=
C
16
By combining 4 CLAs and an LCU together creates a 16-bit adder. Four of these units can be combined to form a 64-bit adder. An additional (second-level) LCU is needed that accepts the propragate (
P
L
C
U
) and generate (
G
L
C
U
) from each LCU and the four carry outputs generated by the second-level LCU are fed into the first-level LCUs.
