Question

Convert −987654321 to (2’s Complement)

Convert 1234.5869 × 10³ to IEEE 745 (show your work)

Convert −98765.4321 to IEEE 745 (show your work)

Convert −98765.4321 to IEEE 745 – double (show your work)

Add 12345869 and −987654321

Add 1234.5869 × 10³ and −98765.4321 (show your work)

Convert 0xc996b4d7 from IEEE 745 to scientific notation (X * 10^Y) (show your work)

Answer 1

1)
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 987654321 successively by 2 until the quotient is 0
   > 987654321/2 = 493827160, remainder is 1
   > 493827160/2 = 246913580, remainder is 0
   > 246913580/2 = 123456790, remainder is 0
   > 123456790/2 = 61728395, remainder is 0
   > 61728395/2 = 30864197, remainder is 1
   > 30864197/2 = 15432098, remainder is 1
   > 15432098/2 = 7716049, remainder is 0
   > 7716049/2 = 3858024, remainder is 1
   > 3858024/2 = 1929012, remainder is 0
   > 1929012/2 = 964506, remainder is 0
   > 964506/2 = 482253, remainder is 0
   > 482253/2 = 241126, remainder is 1
   > 241126/2 = 120563, remainder is 0
   > 120563/2 = 60281, remainder is 1
   > 60281/2 = 30140, remainder is 1
   > 30140/2 = 15070, remainder is 0
   > 15070/2 = 7535, remainder is 0
   > 7535/2 = 3767, remainder is 1
   > 3767/2 = 1883, remainder is 1
   > 1883/2 = 941, remainder is 1
   > 941/2 = 470, remainder is 1
   > 470/2 = 235, remainder is 0
   > 235/2 = 117, remainder is 1
   > 117/2 = 58, remainder is 1
   > 58/2 = 29, remainder is 0
   > 29/2 = 14, remainder is 1
   > 14/2 = 7, remainder is 0
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 111010110111100110100010110001
So, 987654321 of decimal is 111010110111100110100010110001 in binary
Adding 2 zeros on left hand side of this number to make this of length 32
So, 987654321 in normal binary is 00111010110111100110100010110001
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00111010110111100110100010110001 is flipped to 11000101001000011001011101001110
Step 3:. Add 1 to above result
11000101001000011001011101001110 + 1 = 11000101001000011001011101001111
so, -987654321 in 2's complement binary is 11000101001000011001011101001111
Answer: 11000101001000011001011101001111