Microsoft Word - Digital Logic Design v_4_6a

9.5. Adder & Subtractor Design

Small adders can be shown at gate level, but for larger designs we will use an iterative modular design
process. This process allows us to define a circuit for the ith module, and then use it to show the overall
design without redrawing the circuit each time.

 Half Adder

A Half Adder is the simplest form of an adder. It simply treats the carry and binary bit-addition

separately.

 Example: 1-bit adder

 Half Subtractor

A Half Subtractor is the simplest form of Subtractor circuit.

 Example: 1-bit Subtractor

Note: The Half Subtractor is the same as the Half Adder except for one input inversion.

Universally, Subtractor are created by adding additional circuitry to an adders.

 Full Adder

A Full Adder is a set of single bit adders combined to make an n–bit adder. It accepts a carry

from a lower-significant-digit adder and produces a carry to be used by the next-higher-

significant-digit adder.

 Example:1-bit full adder module design for ith bit.

A 0 Minuend

• B 0 Subtrahend

  ---

  
  

  BO 1 D 0

  
  

Borrow Out

(AND)

Difference Bit

Mod 2 (XOR)

A 0 B 0 B0 1 D 0

0 0 0 0

0 1 1 1

1 0 0 1

1 1 0 0

Half Subtractor Process

Truth Table

A 0

B 0

D 0

BO 1

Gate-level Logic Circuit

A 0

B 0

A

B

S S 0

CO CO 1

HS

Half Subtractor Symbol

A 0

+ B 0

___

CO 1 S 0

Carry Out

(AND)

Sum Bit

Mod 2 (XOR)

A 0 B 0 C0 1 S 0

0 0 0 0

0 1 0 1

1 0 0 1

1 1 1 0

Half Adder Process

Truth Table

A 0

B 0

S 0

CO 1

Gate-level Logic Circuit

A 0

B 0

A

B

S S^0

CO CO 1

HA

Half Adder Symbol