Help me solve this question by using 1's complement
(i) 110(Base2) - 010(Base2)
(ii) 1010(Base2) - 1000(Base2)
Help me solve this question convert The Value -40 and 52 to 8-Bit digit in form of:
(i) Sign and Magnitude
(ii) 1's Complement
(iii) 2's Complement
Sure! Let's start with the first question using 1's complement.
(i) To subtract 010(Base2) from 110(Base2) using 1's complement, we need to take the 1's complement of the number being subtracted (010(Base2)). The 1's complement is obtained by changing all the 0s to 1s and all the 1s to 0s.
So, the 1's complement of 010(Base2) is 101(Base2).
Now, we can perform the subtraction:
110(Base2) - 010(Base2) = 110(Base2) + 101(Base2)
To add the two binary numbers, we can follow these rules:
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 10 (carry 1)
Adding 0 + 0, we get 0.
Adding 1 + 1, we get 10 (carry 1).
So, the result is 010(Base2), which is equal to 2 in decimal.
(ii) Let's perform the second question using 1's complement.
To subtract 1000(Base2) from 1010(Base2), we need to take the 1's complement of the number being subtracted (1000(Base2)).
So, the 1's complement of 1000(Base2) is 0111(Base2).
Now, we can perform the subtraction:
1010(Base2) - 1000(Base2) = 1010(Base2) + 0111(Base2)
Adding the binary numbers according to the rules mentioned earlier, we obtain:
1 + 1 = 10 (carry 1)
1 + 1 = 10 (carry 1)
0 + 0 = 0
0 + 1 = 1
The result is 0110(Base2), which is equal to 6 in decimal.
Now let's move on to the second part of your question: converting -40 and 52 to 8-bit digits in different forms.
(i) In Sign and Magnitude form:
To represent -40 in sign and magnitude form, we need to allocate 1 bit for the sign and 7 bits for the magnitude. The leftmost bit will represent the sign, where 0 represents a positive number and 1 represents a negative number. For the magnitude, we will convert 40 to its binary representation, which is 00101000(Base2). Therefore, -40 in sign and magnitude form is:
110101000(Base2), where the leftmost bit is the sign bit (1) and the remaining 7 bits represent the magnitude.
To represent 52 in sign and magnitude form, we convert 52 to binary representation, which is 00110100(Base2). Since 52 is a positive number, the leftmost bit will be 0. Therefore, 52 in sign and magnitude form is:
00110100(Base2), where the leftmost bit is the sign bit (0) and the remaining 7 bits represent the magnitude.
(ii) In 1's Complement form:
To represent -40 in 1's complement form, we need to compute the 1's complement of its binary representation, which is:
-40 = 110101000(Base2) in sign and magnitude form.
To find the 1's complement, we flip all the bits of -40's binary representation:
001010111(Base2). Therefore, -40 in 1's complement form is:
101010111(Base2).
To represent 52 in 1's complement form, we convert 52 to binary representation, which is 00110100(Base2). Since 52 is a positive number, the 1's complement will be the same as the binary representation itself. Therefore, 52 in 1's complement form is:
00110100(Base2).
(iii) In 2's Complement form:
To represent -40 in 2's complement form, we need to compute the 2's complement of its binary representation, which is obtained by first finding the 1's complement and then adding 1 to it.
-40 = 110101000(Base2) in sign and magnitude form.
To find the 1's complement, we flip all the bits of -40's binary representation:
001010111(Base2).
Now, to find the 2's complement, we add 1 to the 1's complement:
001010111(Base2) + 1 = 001011000(Base2).
Therefore, -40 in 2's complement form is:
11011000(Base2).
To represent 52 in 2's complement form, we convert 52 to binary representation, which is 00110100(Base2). Since 52 is a positive number, the 2's complement will be the same as the binary representation itself. Therefore, 52 in 2's complement form is:
00110100(Base2).
I hope this helps! Let me know if you have any further questions.