Question

Show the decimal integer -143 in 10-bit sign magnitude, one's complement, two's complement and excess-511 respectively in the given order

Answer 1

-143
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This is negative. so, follow these steps to convert this to various binary formats.
Divide 143 successively by 2 until the quotient is 0
143/2 = 71, remainder is 1
71/2 = 35, remainder is 1
35/2 = 17, remainder is 1
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 10001111
Adding 2 zeros on left hand side of this number to make this of length 10
So, 143 in normal binary format is 0010001111
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 0010001111 becomes 1010001111
=======================================
||    sign-magnitude: 1010001111    ||
=======================================

1's complement:
-----------------
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   0010001111 is flipped to 1101110000
=======================================
||    1's complement: 1101110000    ||
=======================================

2's complement:
-----------------
Add 1 to above result
1101110000 + 1 = 1101110001
=======================================
||    2's complement: 1101110001    ||
=======================================

excess-511:
------------
for excess 511, add 511 to -143
-143+511 = 368
convert 368 to 10-bit binary
Divide 368 successively by 2 until the quotient is 0
368/2 = 184, remainder is 0
184/2 = 92, remainder is 0
92/2 = 46, remainder is 0
46/2 = 23, remainder is 0
23/2 = 11, remainder is 1
11/2 = 5, remainder is 1
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 101110000
Adding 1 zeros on left hand side of this number to make this of length 10
368 in binary is 0101110000
excess-511: 0101110000