Question

6) What is the 6-bit 1's complement representation of -17₁₀?

Write your answer in the format 0bXXXX... Where X's are binary digits. Include leading 0's (zeroes).

7)  What is the 6-bit sign-magnitude representation of -17₁₀?

Write your answer in the format 0bXXXX... Where X's are binary digits. Include leading 0's (zeroes).

9)  What is the 8-bit 1's complement representation of 17₁₀?

Write your answer in the format 0xHHHH... Where H's are hexidecimal digits. Include leading 0's (zeroes). Write hexidecimal digits, A-F, in capitals.

10)  What is the 8-bit sign-magnitude representation of 17₁₀?

Write your answer in the format 0xHHHH... Where H's are hexidecimal digits. Include leading 0's (zeroes). Write hexidecimal digits, A-F, in capitals.

Answer 1

6)
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 17 successively by 2 until the quotient 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 10001
So, 17 of decimal is 10001 in binary
Adding 1 zeros on left hand side of this number to make this of length 6
So, 17 in normal binary is 010001
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   010001 is flipped to 101110
so, -17 in 1's complement binary is 101110
Adding 2 zeros on left hand side of this number to make it's length a multiple of 4
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from binary to hexadecimal
Converting 00101110 to hexadecimal
0010 => 2
1110 => E
So, in hexadecimal 00101110 is 0x2E
Answer: 0x2E

7)
-17
------
This is negative. so, follow these steps to convert this to various binary formats.
Divide 17 successively by 2 until the quotient 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 10001
So, 17 of decimal is 10001 in binary
Adding 1 zeros on left hand side of this number to make this of length 6
So, 17 in normal binary format is 010001
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 010001 becomes 110001
===================================
||    sign-magnitude: 110001    ||
===================================
Converting 00110001 to hexadecimal
0011 => 3
0001 => 1
So, in hexadecimal 00110001 is 0x31
Answer:  0x31

8)
Since this is a positive number. we can directly convert this into binary
Divide 17 successively by 2 until the quotient 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 10001
So, 17 of decimal is 10001 in binary
Adding 3 zeros on left hand side of this number to make this of length 8
so, 17 in 1's complement binary is 00010001
Converting 00010001 to hexadecimal
0001 => 1
0001 => 1
So, in hexadecimal 00010001 is 0x11
Answer: 0x11

9)
17
-----
Since this is a positive number. we can directly convert this into binary
Divide 17 successively by 2 until the quotient 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 10001
So, 17 of decimal is 10001 in binary
Adding 3 zero(s) on left hand side of this number to make this of length 8
So, 17 in normal binary format is 00010001
=====================================
||    sign-magnitude: 00010001    ||
=====================================
Converting 00010001 to hexadecimal
0001 => 1
0001 => 1
So, in hexadecimal 00010001 is 0x11
Answer: 0x11