use binary addition
1)13base10+2base10
13base10 = 1101base2
2base10 = 0010base2
1101
+ 0010
------
1111base2
Therefore, 13base10 + 2base10 = 15base10 or 1111base2.
state one use of hexadecimal notation a computer
One use of hexadecimal notation in a computer is to represent memory addresses. Memory addresses are typically expressed in hexadecimal notation because it allows programmers to represent them in a shorter form that is easier to read and write than binary. Additionally, hexadecimal notation maps nicely to the byte-addressable memory architecture used in modern computers, making it a natural choice for computer memory addressing.
use ones compliment the solve the following
1)9-6
2)17-15
3)1110-1011
4)111010-110011
To use ones' complement to solve the following problems, we first need to convert the numbers to binary and then take the ones' complement of the subtrahend.
1) 9 - 6
9base10 = 1001base2
6base10 = 0110base2
To get the ones' complement of the subtrahend (6), we invert all the bits:
0110 -> 1001
Now we can perform the subtraction:
1001
+ 1001
-------
0010
Since the result is positive (the leftmost bit is a 0), the answer is 0010base2 which is 2base10.
2) 17 - 15
17base10 = 0001 0001base2
15base10 = 0000 1111base2
The ones' complement of 15 is:
0000 1111 -> 1111 0000
Now we can perform the subtraction:
0001 0001
+ 1111 0000
----------
0000 0001
Since the result is positive, the answer is 0001base2 which is 1base10.
3) 1110 - 1011
1110base2 = 14base10
1011base2 = 11base10
The ones' complement of 1011 is:
1011 -> 0100
Now we can perform the subtraction:
1110
+ 0100
-------
0010
Since the result is positive, the answer is 0010base2 which is 2base10.
4) 111010 - 110011
111010base2 = 58base10
110011base2 = 51base10
The ones' complement of 110011 is:
110011 -> 001100
Now we can perform the subtraction:
111010
+ 001100
--------
100111
Since the result is negative (the leftmost bit is a 1), we take the ones' complement of the result to get the answer:
100111 -> 011000
Since the leftmost bit of the ones' complement is 0, the answer is positive, so the answer is 011000base2 which is 24base10.
To add two numbers in binary, you follow the same principles as adding numbers in decimal. Here's how you would add 13 (in base 10) and 2 (in base 10) using binary addition.
Step 1: Convert 13 and 2 to binary.
- 13 in binary is 1101.
- 2 in binary is 0010.
Step 2: Align the binary numbers.
- Write them down beneath each other, aligning them so that the least significant bits (rightmost digits) are in the same column.
1101
+ 0010
Step 3: Perform the addition.
- Starting from the rightmost column, add the bits vertically and carry over any resulting sums that are equal to or greater than 2.
1101
+ 0010
-------
1111
Step 4: Write down the result.
- The sum of 13 and 2 in binary is 1111.
Therefore, 13base10 + 2base10 = 1111base2.