quick.gif

space2.gif

space2.gif

space2.gif

space2.gif

space2.gif

space2.gif

space2.gif

   

space.gif

   

space.gif

  ../images/main/bullet_green_ball.gif Introduction

Arithmetic circuits are the ones which perform arithmetic operations like addition, subtraction, multiplication, division, parity calculation. Most of the time, designing these circuits is the same as designing muxers, encoders and decoders.

   

space.gif

In the next few pages we will see few of these circuits in detail.

   

space.gif

  ../images/main/bullet_green_ball.gif Adders

Adders are the basic building blocks of all arithmetic circuits; adders add two binary numbers and give out sum and carry as output. Basically we have two types of adders.

   

space.gif

  • Half Adder.
  • Full Adder.
   

space.gif

   

space.gif

  ../images/main/bulllet_4dots_orange.gif Half Adder

Adding two single-bit binary values X, Y produces a sum S bit and a carry out C-out bit. This operation is called half addition and the circuit to realize it is called a half adder.

   

space.gif

Truth Table

X

Y

SUM

CARRY

0

0

0

0

0

1

1

0

1

0

1

0

1

1

0

1

   

space.gif

Symbol

   

space.gif

../images/digital/half_adder_block.gif
   

space.gif

S (X,Y) = (1,2)

S = X'Y + XY'

S = XY

CARRY(X,Y) = (3)

CARRY = XY

   

space.gif

Circuit

   

space.gif

../images/digital/circuit_half_adder.gif
   

space.gif

  ../images/main/bulllet_4dots_orange.gif Full Adder

Full adder takes a three-bits input. Adding two single-bit binary values X, Y with a carry input bit C-in produces a sum bit S and a carry out C-out bit.

   

space.gif

Truth Table

X

Y

Z

SUM

CARRY

0

0

0

0

0

0

0

1

1

0

0

1

0

1

0

0

1

1

0

1

1

0

0

1

0

1

0

1

0

1

1

1

0

0

1

1

1

1

1

1

   

space.gif

SUM (X,Y,Z) = (1,2,4,7)

CARRY (X,Y,Z) = (3,5,6,7)

   

space.gif

Kmap-SUM

../images/digital/full_adder_kmap_sum.gif
   

space.gif

SUM = X'Y'Z + XY'Z' + X'YZ'

SUM = X Y Z

   

space.gif

Kmap-CARRY

../images/digital/full_adder_kmap_carry.gif
   

space.gif

CARRY = XY + XZ + YZ

   

space.gif

  ../images/main/bullet_star_pink.gif Full Adder using AND-OR

The below implementation shows implementing the full adder with AND-OR gates, instead of using XOR gates. The basis of the circuit below is from the above Kmap.

   

space.gif

Circuit-SUM

../images/digital/full_adder_sum_andor.gif
   

space.gif

Circuit-CARRY

../images/digital/full_adder_carry_andor.gif
   

space.gif

  ../images/main/bullet_star_pink.gif Full Adder using AND-OR
   

space.gif

Circuit-SUM

../images/digital/full_adder_add_ckt.gif.gif
   

space.gif

Circuit-CARRY

../images/digital/full_adder_carry_andor.gif
   

space.gif

   

space.gif

   

space.gif

   

space.gif

space2.gif

space2.gif

space2.gif

space2.gif

space2.gif

  

Copyright 1998-2014

Deepak Kumar Tala - All rights reserved

Do you have any Comment? mail me at:deepak@asic-world.com