Question

Represent (in binary and separately) the decimal signed whole numbers 347 and -347 in each of the following formats:

(a) sign-magnitude.

(b) 1's complement

(c) 2's complement

(d) excess-511

For Parts (a), (b) and (c), use the minimum number of bits necessary; for Part (d), use the same number of bits as in Parts (a), (b) and (c).

CAUTION: You will earn NO CREDITS if you simply show the final result and not clearly show working (i.e., intermediate steps).

(If you use the result from a previous question, indicate the question number and intermediate steps already shown to arrive at that result can be skipped.)

Answer 1

a) 347 in binary is represented as 101011011. In signed magnitude representation, most significant bit represents the sign,0 represents positive sign and 1 represents negative sign. Therefore,

+347 = 0101011011 and -347 = 1101011011

b) In 1's complement Representation, the positive number representation is same as the binary representation and to represent the negative number, take the complement of each bit(change 1 to 0 and 0 to 1)

In 1's complement Representation, using n bits, we can represent -(2^n-1 -1) to +(2^n-1 -1)numbers, so, to represent 347 , no. of bits required are 10

347 = 0101011011 -347 =1010100100

c) In 2's complement Representation, the positive number representation is same as the binary representation and to represent the negative number, we take 2's complement. For 2's complement,we take 1's complement and add 1 to the result .In 2's complement, using n bits, we can represent -(2^n-1 ) to +(2^n-1-1) numbers, so , to represent 347 , no. of bits required are 10

347 = 0101011011

to represent -347, take 1's complement of 347 (0101011011 ) = 1010100100

then add 1 + 1

= 1010100101

-347 =  1010100101

d)Excess 511: 347 = 347+511 = 858 = 1101011010

-347 = -347+511 = 164 = 0010100100