Answer to Question #209381 in Algorithms for Dee

Question

Convert -218 to binary and represent it in Sign-and-Size code

Answer 1

To convert 218(base 10) to binary:

218/2=109 → quotient=109 remainder=0

109/2=54+1 → quotient=54 remainder=1

54/2=27 → quotient=27 remainder=0

27/2=13+1 → quotient=13 remainder=1

13/2=6+1 → quotient=6 remainder=1

6/2=3 → quotient=3 remainder=0

3/2=1+1 → quotient=1 remainder=1

1/2=0+1 → quotient=0 remainder=1

So

$218_{10}=1\cdot2^7+1\cdot2^6+0\cdot2^5+1\cdot2^4+1\cdot2^3+0\cdot2^2+1\cdot2^1+0\cdot2^0=11011010_2$

There are three types of representations for signed binary numbers. These are: Sign-Magnitude form, 1’s complement form, and 2’s complement form.

Sign-Magnitude form: for negative n bit binary numbers, the most significant sign bit is 1

1’s complement form: the 1's complement form of a negative binary number is the bitwise NOT applied to it (the 'complement' of its positive counterpart)

2’s complement form: negative numbers are represented by the bit pattern which is one greater than the 1's complement

Answer: Sign 1 and Size 11011010 code