Microsoft Word - Digital Logic Design v_4_6a

 Ripple-Carry Adder (RCA)

A Ripple-Carry Adder uses Full Adders in a cascading form. The carry from one adder is fed to

the next most significant bit-adder.

 The Ripple-Carry Adder will have to wait until all the carries have propagated through the

circuit before output stabilizes and results are valid. Carry-Look-ahead or carry-anticipation is

often used to speed up the addition.

 Indirect Subtraction

Given the following facts, a Subtractor can be designed from an RCA:

 Given A – B = A + (-B)

 From the two’s complement, (-B)2RC =B+ 1

 Use an XOR to invert B when SUB=1 (subtraction) and B when SUB=0 (addition).

A B CI

S 0

FA0

CO S

A0 B0 CI

A B CI

S 1

FA1

CO S

A1 B1 CI

A B CI

S 2

FA2

CO S

A2 B2 CI

A B CI

S 3

FA3

CO S

A3 B3 CI

CO

”Overflow”

GND

CI Carry In

A Operand 1

+ B Operand 2

________

CO S 0

Carry Out

Sum Bit

CI A B C0 S

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Full Adder Process Truth Table

CI

A 0

B 0

CI

A

B

S S^0

CO CO 1

FA

Full Adder Symbol

0 0

1 1

0 1

0 1

CI, A B^ 0 1^

00

01

11

10

Carry Out CO =

A.B + CI.A + CI.B

0 1

0 1

1 0

1 0

B (^) 0 1
00
01
11
10
Sum Bit S = A⊕B⊕C

CI, A

CI

A

B

S

CO

Full Adder Circuit