Question

1. Complete the matrix below (use 4 bits)

Signed Integer	Signed Magnitude		1’s Complement	2’s Complement	Excess-7
5
-3

Answer 1

5   -   0101    -   0101    -   0101    -   1100
-3  -   1011    -   1100    -   1101    -   0100

1)
5
----
Since this is a positive number. we can directly convert this into binary
Divide 5 successively by 2 until the quotient is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 101
So, 5 of decimal is 101 in binary
So, 5 in normal binary format is 0101
=================================
||    1's complement: 0101    ||
||    2's complement: 0101    ||
||    sign-magnitude: 0101    ||
=================================

Converting 5 to excess-7
add excess to number
5 + 7 = 12
convert 12 to binary
Divide 12 successively by 2 until the quotient is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1100
So, 12 of decimal is 1100 in binary
Excess-7:   1100

2)
-3
-----
This is negative. so, follow these steps to convert this to various binary formats.
Divide 3 successively by 2 until the quotient is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11
So, 3 of decimal is 11 in binary
So, 3 in normal binary format is 0011
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 0011 becomes 1011
=================================
||    sign-magnitude: 1011    ||
=================================

1's complement:
-----------------
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   0011 is flipped to 1100
=================================
||    1's complement: 1100    ||
=================================

2's complement:
-----------------
Add 1 to above result
1100 + 1 = 1101
=================================
||    2's complement: 1101    ||
=================================

Converting -3 to excess-7
add excess to number
-3 + 7 = 4
convert 4 to binary
Divide 4 successively by 2 until the quotient 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 100
So, 4 of decimal is 0100 in binary
Excess-7:   0100