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Convert the number -120 into 8 bit two's complement. - Scottish Highers Computing Science - Question 1 - 2018
Question 1
Convert the number -120 into 8 bit two's complement.
Worked Solution & Example Answer:Convert the number -120 into 8 bit two's complement. - Scottish Highers Computing Science - Question 1 - 2018
Step 1
Step 1: Convert 120 to Binary
Answer
To convert the positive number 120 into binary, we can divide the number by 2 and record the remainders:
120 ÷ 2 = 60, remainder 0
60 ÷ 2 = 30, remainder 0
30 ÷ 2 = 15, remainder 0
15 ÷ 2 = 7, remainder 1
7 ÷ 2 = 3, remainder 1
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, we get:
120 = 01111000 (in binary)
Step 2
Step 2: Find the Two's Complement
Answer
To find the two's complement of a binary number, we follow these steps:
- Invert the bits (change 0 to 1 and 1 to 0).
- Add 1 to the inverted binary number.
Start with the binary representation of 120:
01111000
Inverting the bits gives:
10000111
Now, add 1:
10000111
+ 1
---------
10001000
Thus, the two's complement of -120 is:
10001000