Question Find the complement of the binary number . Calculate the magnitude and show all steps.
Studdy Solution
STEP 1
Assumptions
1. The given number is a binary number: 1010101.
2. The complement referred to here is the binary complement, which is often the two's complement.
3. The magnitude of a binary number is its decimal equivalent.
4. To find the two's complement, we first find the one's complement by flipping the bits and then add 1 to the least significant bit (LSB).
STEP 2
First, we need to calculate the magnitude of the given binary number by converting it to its decimal equivalent.
STEP 3
Now, calculate the magnitude by evaluating the powers of 2 for each bit where the bit is 1.
STEP 4
Add the values where the binary digit is 1.
STEP 5
Calculate the sum to find the magnitude in decimal.
STEP 6
Now we will find the one's complement of the binary number by flipping all the bits.
STEP 7
Finally, we add 1 to the least significant bit (LSB) of the one's complement to find the two's complement.
The complement of the binary number 1010101 is 0101011, and the magnitude of the original number is 85.
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