What's the importance of 10's, 9's, 2's and 1's complements?

[kreisa]

Okay, I know how to solve for them. But I'm a noob when it comes to electronics. I'm kinda curious, just why is there a need to study complements? I don't get it.

I can't see the connection between hardware (wires, resistors etc) and complements. I'm confused! Help me! My teacher failed to explain why we need to study this. I know it's important, but it's not really that clear to me right now.

Please shed some light to this noob.

T_T
Thanks.

 

[srizbf]

Re: What's the importance of 10's, 9's, 2's and 1's compleme

when you have a complement of a number , that can be used in subtraction process.

eg. 8-3=5
take 10's complement of 3.
9-3=6
6+1=7. ie 7 is 10s complement of 3. right?

now , in the subtraction of '8-3'
use 10's complement of 3 and 'ADD'

eg:8+7=15
discard carry . result is 5 which is '8-3'

point is instead of subtracting you add .
in hardware , you use only adder to subtarct.
clear?

 

[alaparthi]

Re: What's the importance of 10's, 9's, 2's and 1's compleme

Hi,

Understanding Binary Numbers and the related Math is very important to deal with digital electronics. Complements are also part of Binary Math.

I can think of one immediate application for 2's complement.

Suppose, if you need to subtract a binary number, say 'B' from 'A'. Each 4 bit numbers.
That is , Y = A-B.
Note that Y is 5-bit number.

You can find 2's complement of B, say B' and add it to A.
Y = A + B'

Suppose, now you need to implement a circuit to do this.
You are given a 4-bit Adder and 4 XOR Gates. Based on a select input (S) you need to either Add or Subtract.
How do you design?