Obtain Binary String: X + Y - Z | Binary Addition and Subtraction Rules

[rclakmal]

Obtain Binary String ?

Homework Statement

Given That X=10111 ,Y=101; Z=1001, obtain binary strings that represent P Q where
P=X+Y and Q=P-Z; state clearly each rule you apply .

Homework Equations

The Attempt at a Solution

Hey up to the extent which i know i did this as a normal binary addition and subtractions >then i got P=10010
and Q=1001 .But the problem is I am not sure that i have used any kind of rules here. or Have I ?? Or did i made a mistake in interpreting the problem .Can somebody help . this is all u got for that question ,i have included all the details.

 

[Mark44]

Doing binary addition, I get a different result for P. The addition rules in binary are:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10

I can't think of any rules other than these.

So for X + Y you have
10111
+ 101
-----
11100

 

[Architeuthis Dux]

Hi there,

To obtain the binary string P, you can use the binary addition rule. This rule states that when adding two binary numbers, you start from the right and work your way to the left, adding each column and carrying over any extra 1's.

So in this case, you would start with the rightmost column and add 1+1, which gives you 0 and a carryover of 1. Then you move to the next column and add 1+0+1, which gives you 0 and a carryover of 1 again. You continue this process until you have added all the columns and end up with P=10010.

To obtain the binary string Q, you can use the binary subtraction rule. This rule states that when subtracting two binary numbers, you start from the right and work your way to the left, subtracting each column and borrowing from the next column if necessary.

So in this case, you start with the rightmost column and subtract 1-1, which gives you 0. Then you move to the next column and subtract 1-0-1, which gives you 0 and you borrow 1 from the next column. You continue this process until you have subtracted all the columns and end up with Q=1001.

I hope this helps! Let me know if you have any further questions.