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P-1 Adders & Subtractors & Adder-Subtractor & Incrementer & Decrementer

posted Nov 4, 2012, 12:53 AM by Neil Mathew   [ updated Nov 4, 2012, 1:23 AM ]

We've done this countless times in so many different ways.

That said, I say it's easier if I just mention the functions used:

NOT    7404
AND    7408
OR      7432
XOR   7486



HALF 
ADDER

Sum=A XOR B

Carry=A AND B

FULL
ADDER


Sum=A XOR B XOR Cin

Carry=(A AND B) OR (B AND Cin) OR (Cin AND A)
 
HALF
SUBTRACTOR

D=X XOR Y

B=(NOT X) AND Y



FULL 
SUBTRACTOR

D=X XOR Y XOR Z

B=(NOT X AND Y) OR (NOT X AND Z) OR (Y AND Z)

Full-Subtractor Circuit



Binary Adder-Subtractor Circuit

Take a good look at the circuit:


Here the [+] are the full adders. 

Use the clock as M to control whether it adds or not.
That is, when m=0 it acts as an ADDER
And when m=1 it acts as a SUBTRACTOR

To get the B' + 1 (2's complement) we use the XOR Gate.
B (+) 0 = B
B (+) 1 = B'

Since making each of the four full adder circuits is gonna take time, we use ICs.
7483A ( 4-BIT BINARY FULL-ADDER CIRCUIT)

Incrementer & Decrementer

We can do these in two ways.

Option 1:
Use a 4-Bit Half-Adder circuit where the Carry(in) = 1
(but we'll have to create each half-adder circuit separately = tedious)



Option 2: 
Use the 4-Bit Full-Adder IC (7483A)


For Incrementer: B = 0001
For Decrementer: B= 1111


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