Arithmetic Hardware

1) Half Adder:

It is a device with two incomes to which goes applied the bit brace to add, a Xor door supplies the sum while same the two incomes apply you to a And supply the Carry out.

 

2) Full Adder:

It is a device with three incomes, two relati to you to the bit to add and relative to the Carry obtained from the Full relative Adder to the brace of immediately previous bit, inner it is constituted from two Half Adder, the first one generates the carry inner, it executes the sum of the bit brace and it sendes it to according to Half Adder having as 2° income Carry-In in escape from it has the complete sum and the 2° carry inner of which it is necessary to make the Or with the previous one in order to obtain the Carry-Out of this door. For semplicità the circuit can be realized with of the Nand doors in place of the And and of the OR.

 

3) Carry Ripple Adder:

Bit executes the sum of two 4 binary figures to, Full Adder is constituted from 4 connects to you so that Carry-In of the first one it is fixed to 0 logical while its Carry-Out is connected to Carry-In of the successive one and cos¬ via. The defect of this configuration is that before that it is possible to make the last sum it is necessary that the Carry generated from the Full Adder is available previous.

 

4) Carry Look-Ahead Adder:

It is a sommatore that it tries to diminish the time of elaboration immediately rendering available the Carry for ognuna of the braces of bit adding. The realizzativo outline is constituted from 4 Half Adder that they supply marks them:

Propagate that is 1 solo when a single bit of the income brace is 1

Generate that is 1 solo when both the incomes are to 1

to a said circuit Look-Ahead Generator which she supplies directly in parallel the Carry relative you to the 4 braces of bit to add, Making the Xor between everyone of these and the correspondent it marks them of Propagate obtains the complete sum of Carry. Naturally the semplicità of I use of the satisfied CLG in terms of complexity and time of elaboration of the same one that is approximately 4 times the time of propagation in one Nand door.