Question

Please show all work:

Determine the 2’s complement equivalent of the following numbers in 8-bit format (N.B: You must show your work for full credit)!

1. -12 =
2. -9 =

Answer 1

1)Bit is the smallest unit in computers world.
2) 8 bit number means combinations of 0_s and 1s.

For -12

For 2's complement we need two follow some rules

• Convert the decimal number into binary number
• apply 1s complement on binary number
• and to the result of 1s complement add 1 (binary addition)

step 1) convert 12 in binary

12=00001100

replace left most bit with 1 two make it negative

-12 = 10001100

step 2) convert it into ones complement

for this you need to invert the given number (replace 1 by 0 and 0 by 1)

1's complement =

01110011

step 3) Add 1 to 1s complemt to convert it into 2's complement. (Binary addition are used and not normal mathematical addition because we are dealing in bits )

01110011

+1

01110100 ans

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For -9

For 2's complement we need to follow some rules

• Convert the decimal number into binary number
• apply 1s complement on binary number
• and to the result of 1s complement add 1 (binary addition)

step 1) convert 9 in binary  

9 = 00001001

replace left most bit with 1 two make it negative

-9= 10001001

step 2) convert it into ones complement

for this you need to invert the given number (replace 1 by 0 and 0 by 1)

1's complement = 01110110

step 3) Add 1 to 1s complemt to convert it into 2's complement. (Binary addition are used and not normal mathematical addition because we are dealing in bits )

2's complement =

01110110

+1

01110111