Question

convert +38 and +17 to binary using the signed 2s complement representation and enough digits to accomaodate the numbers. Then perform the binary equivalent of (-38) and +17

Answer 1

Calculating 38 in binary:
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Write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

38 /  2  result 19 remainder  0
19 /  2  result 9  remainder  1
9  /  2  result 4  remainder  1
4  /  2  result 2  remainder  0
2  /  2  result 1  remainder  0
1  /  2  result 0  remainder  1

Read the remainders from bottom to top.

( 38 )10 = ( 100110 )2

So, fill zeros to the front to make it 8 bit

( 38 )10 = ( 00100110 )2

Ones complement = Inverting all the bits in binary
                = 11011001
Twos complement = Ones complement + 1
                = 11011001 + 1
                = 11011010

So, -38 in binary is 11011010

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Calculating 17 in binary:
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Write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

17 /  2  result 8  remainder  1
8  /  2  result 4  remainder  0
4  /  2  result 2  remainder  0
2  /  2  result 1  remainder  0
1  /  2  result 0  remainder  1

Read the remainders from bottom to top.

( 17 )10 = ( 10001 )2

So, fill zeros to the front to make it 8 bit

( 17 )10 = ( 00010001 )2

So, 17 in binary is 00010001

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Calculating -38+17 =
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  11011010
+ 00010001
------------
  11101011
------------

So, the result of -38+17 in binary is 11101011

we have to convert 11101011 back to decimal to make answer in decimal
As MSB is 1, this is in two's complement

Ones complement = Twos complement - 1
                = 11101011 - 1
                = 11101010
Binary = -Inverting all the bits in binary
       = -00010101
So, The decimal value of 00010101 is 21

So, 11101011 in decimal is -21

Final Answer in binary is 11101011
Final Answer in decimal is -21