Question

Binary

How is 00001001 (base 2) represented in 8-bit two’s complement notation?

Convert 0.3828125 to binary with 4 bits to the right of the binary point.

How is 00110100 (base 2) represented in 8-bit one's complement.  

Answer 1

1)
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00001001 is flipped to 11110110
Add 1 to above result
11110110 + 1 = 11110111
Answer: 11110111

2)
Converting 0.3828125 to binary
Convert decimal part first, then the fractional part
> First convert 0 to binary
Divide 0 successively by 2 until the quotient is 0
Read remainders from the bottom to top as
So, 0 of decimal is  in binary
> Now, Convert 0.38281250 to binary
   > Multiply 0.38281250 with 2. Since 0.76562500 is < 1. then add 0 to result
   > Multiply 0.76562500 with 2. Since 1.53125000 is >= 1. then add 1 to result
   > Multiply 0.53125000 with 2. Since 1.06250000 is >= 1. then add 1 to result
   > Multiply 0.06250000 with 2. Since 0.12500000 is < 1. then add 0 to result
   > Multiply 0.12500000 with 2. Since 0.25000000 is < 1. then add 0 to result
   > Multiply 0.25000000 with 2. Since 0.50000000 is < 1. then add 0 to result
   > Multiply 0.50000000 with 2. Since 1.00000000 is >= 1. then add 1 to result
   > This is equal to 1, so, stop calculating
0.3828125 of decimal is 0.0110001 in binary
so, 0.3828125 in binary is 0.0110001
if you need only 4 bits, answer is 0.0110
Answer: 0.0110

3)
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00110100 is flipped to 11001011
Answer: 11001011