Question

1) Represent -34 and +67 in the following ways: a) 8 bit sign and magnitude representation with MSB as sign bit. b) 8 bit 1’s complement representation. c) 8 bit 2’s complement representation. 2) Convert the decimal numbers 40 and 20 into 8-bit unsigned binary representation and add the two numbers.

Answer 1

1)
a)
-34
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This is negative. so, follow these steps to convert this to various binary formats.
Divide 34 successively by 2 until the quotient is 0
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 100010
Adding 2 zeros on left hand side of this number to make this of length 8
So, 34 in normal binary format is 00100010
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 00100010 becomes 10100010
=====================================
||    sign-magnitude: 10100010    ||
=====================================

1's complement:
-----------------
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00100010 is flipped to 11011101
=====================================
||    1's complement: 11011101    ||
=====================================

2's complement:
-----------------
Add 1 to above result
11011101 + 1 = 11011110
=====================================
||    2's complement: 11011110    ||
=====================================

b)
67
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Since this is a positive number. we can directly convert this into binary
Divide 67 successively by 2 until the quotient is 0
67/2 = 33, remainder is 1
33/2 = 16, remainder is 1
16/2 = 8, remainder is 0
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 1000011
Adding 1 zero(s) on left hand side of this number to make this of length 8
So, 67 in normal binary format is 01000011
=====================================
||    1's complement: 01000011    ||
||    2's complement: 01000011    ||
||    sign-magnitude: 01000011    ||
=====================================