Lookahead Carry Unit

Lookahead Carry Unit

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).

16-bit adder

By combining four 4-bit CLAs, a 16-bit adder can be created but additional logic is needed in the form of an LCU.A single 4-bit CLA is shown below:

The LCU accepts the group propagate (PG) and group generate (GG) from each of the four CLAs.The LCU then generates the carry input for each CLA.

Assume that P_i is PG and G_i is GG from the ith CLA then the output carry bits are

:C_{4} = G_0 + P_0 cdot C_0:C_{8} = G_{4} + P_{4} cdot C_{4}:C_{12} = G_{8} + P_{8} cdot C_{8}:C_{16} = G_{12} + P_{12} cdot 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 cdot C_0:C_{8} = G_4 + G_0 cdot P_4 + C_0 cdot P_0 cdot P_4:C_{12} = G_8 + G_4 cdot P_8 + G_0 cdot P_4 cdot P_8 + C_0 cdot P_0 cdot P_4 cdot P_8:C_{16} = G_{12} + G_8 cdot P_{12} + G_4 cdot P_8 cdot P_{12} + G_0 cdot P_4 cdot P_8 cdot P_{12} + C_0 cdot P_0 cdot P_4 cdot P_8 cdot 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_{LCU} = P_0 cdot P_4 cdot P_8 cdot P_{12}:G_{LCU} = G_{12} + G_8 cdot P_{12} + G_4 cdot P_{12} cdot P_8 + G_0 cdot P_{12} cdot P_8 cdot P_4

64-bit adder

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 propagate (P_{LCU}) and generate (G_{LCU}) from each LCU and the four carry outputs generated by the second-level LCU are fed into the first-level LCUs.

References

*


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Carry-lookahead adder — 4 bit adder with carry lookahead A carry lookahead adder (CLA) is a type of adder used in digital logic. A carry lookahead adder improves speed by reducing the amount of time required to determine carry bits. It can be contrasted with the simpler …   Wikipedia

  • Carry look-ahead adder — A carry look ahead adder is a type of adder used in digital logic. It can be contrasted with the simpler, but usually slower, ripple carry adder ( see adder for detail on ripple carry adders ). A ripple carry adder works in the same way as pencil …   Wikipedia

  • Adder (electronics) — In electronics, an adder or summer is a digital circuit that performs addition of numbers.In modern computers adders reside in the arithmetic logic unit (ALU) where other operations are performed.Although adders can be constructed for many… …   Wikipedia

  • Схема ускоренного переноса — Необходимо проверить качество перевода и привести статью в соответствие со стилистическими правилами Википедии. Вы можете помочь …   Википедия

  • LCU — may refer to:* Landing Craft Utility * Lubbock Christian University * Lookahead Carry Unit * Local currency unit * Local colleges and universities in the Philippines * Least Competent User Usability testing …   Wikipedia

  • List of 7400 series integrated circuits — The following is a list of 7400 series digital logic integrated circuits. The 7400 series originated with TTL integrated circuits made by Texas Instruments. Because of the popularity of these parts, they were second sourced by other manufacturers …   Wikipedia

  • Redundant binary representation — A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. RBR is unlike usual binary numeral systems, including two s… …   Wikipedia

  • Addition — is the mathematical process of putting things together. The plus sign + means that two numbers are added together. For example, in the picture on the right, there are 3 + 2 apples meaning three apples and two other apples which is the same as… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”