Question

Please show all work and please explain what a 5 bit excess is.
3) Convert the following decimal number to binary 

   554

5) What is the range of 5-bit excess-16 numbers? 

6) What is the range of 5-bit two's complement numbers?

7) What is the range of 5-bit unsigned numbers?

8) What is the range of 5-bit sign-magnitude numbers?

Answer 1

3)
Divide 554 successively by 2 until the quotient is 0
   > 554/2 = 277, remainder is 0
   > 277/2 = 138, remainder is 1
   > 138/2 = 69, remainder is 0
   > 69/2 = 34, remainder is 1
   > 34/2 = 17, remainder is 0
   > 17/2 = 8, remainder is 1
   > 8/2 = 4, remainder is 0
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1000101010
So, 554 of decimal is 1000101010 in binary
Answer: 1000101010

5)
normal range of 5-bit binary is 0 to 31
in excess-16 just subtract 16 from the above range
0-16 to 31-16
=>  -16 to 15
Answer: -16 to 15

6)
range in 2's complement is -2^4 to 2^4 - 1
=>  -16 to 16-1
=>  -16 to 15
Answer: -16 to 15

7)
range in unsigned numbers is 0 to 2^5-1
=>  0 to 32-1
=>  0 to 31
Answer: 0 to 31

8)
range in signed-magnitude is -2^4 + 1 to 2^4 - 1
=>  -16+1 to 16-1
=>  -15 to 15
Answer: -15 to 15