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CMOS Adder s Architecture 1

2. Contents. Half Adder (HA)Full Adder (FA)Sign Bit OverflowRipple Carry Adder (RCA)Carry Lookahead Adder (CLA). * Reference: K.S.Yeo, Low-Voltage, Low-Power VLSI Subsystems, McGraw-Hill, 2005: J. P. Deschamps, Synthesis of Arithmetic Circuits, John Wiley

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CMOS Adder s Architecture 1

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    1. CMOS Adder’s Architecture (1)

    2. 2 Contents Half Adder (HA) Full Adder (FA) Sign Bit Overflow Ripple Carry Adder (RCA) Carry Lookahead Adder (CLA)

    3. 3 Half Adder (1) Half Adder (HA) Inputs : Pair of single-bits but no a carry-in Truth Table Logic functions

    4. 4 Half Adder (2)

    5. 5 Full Adder (1) Full Adder (FA) Inputs : Two binary numbers and a Carry-in Truth Table

    6. 6 Full Adder (2) Karnaugh Map

    7. 7 Full Adder (3) Logic circuits of Full Adder

    8. 8 Full Adder (4)

    9. 9 Sign Bit Overflow (1) An erroneous carry into the sign bit of a signed binary number that results from a sum or difference larger than can be represented by the number of magnitude bits In unsigned addition, the binary equivalent is In signed addition, the sum is the same but has a different meaning. The sum of positive signed binary numbers Must not exceed 2n-1-1 for numbers having n magnitude bits Otherwise, there will be an overflow into the sign bit

    10. 10 Sign Bit Overflow (2) Overflow Detection Requires access to the sign bits of the operands and result If the sign bits of both operands are the same and the sign bit of sum is different from the operand sign bits, ?An overflow has occurred

    11. 11 Sign Bit Overflow (3) The Boolean expression for the overflow detector is:

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    22. 22 Carry Lookahead Adder (5) 16-bit Carry Look ahead Adder Block diagram using 4-bit CLA

    23. 23 Carry Lookahead Adder (6) Carry Generation Logic Where

    24. 24 Carry Lookahead Adder (8) Carry Generation using Group Carry Generate and Propagate Function

    25. 25 Carry Lookahead Adder (7) Carry Generation Logic

    26. 26 Carry Lookahead Adder (8)

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