Write down the six bit sign magnitude notation for:
A.(+7)10 and (-7)10
B.Write the 2’s Complement for (-7)10
A.
(+7)10 = 0111 in sign magnitude notation
(-7)10 = 1111 in sign magnitude notation
B. The 2's complement of (-7)10 is calculated by taking the 1's complement (flipping all the bits) and then adding 1.
1's complement of (-7)10:
-7 in binary = 1111
1's complement = 0000
Adding 1 to the 1's complement:
0000 + 1 = 0001
Therefore, the 2's complement of (-7)10 is 0001.
A. To represent numbers in sign magnitude notation, we use six bits. The leftmost bit represents the sign, where 0 denotes a positive number and 1 denotes a negative number. The remaining 5 bits represent the magnitude of the number.
a. For (+7)10:
Step 1: Determine the sign. Since (+7)10 is positive, the sign is 0.
Step 2: Convert the magnitude of the number (7)10 to binary. (7)10 = (0111)2.
Step 3: Combine the sign and magnitude. The sign is 0 and the magnitude is 0111, so the sign-magnitude notation for (+7)10 is 00111.
b. For (-7)10:
Step 1: Determine the sign. Since (-7)10 is negative, the sign is 1.
Step 2: Convert the magnitude of the number (7)10 to binary. (7)10 = (0111)2.
Step 3: Combine the sign and magnitude. The sign is 1 and the magnitude is 0111, so the sign-magnitude notation for (-7)10 is 10111.
B. To find the 2's complement of a negative number, we need to flip the bits and add 1.
For (-7)10:
Step 1: Convert the magnitude of the number (7)10 to binary. (7)10 = (0111)2.
Step 2: Flip the bits. The flipped bits are (1000).
Step 3: Add 1. Adding 1 to (1000) gives us (1001).
Step 4: The resulting value is the 2's complement of (-7)10, which is (1001)2.