Mark each of the following statements as true/false Signed-magnitude and two\'s

Question

Mark each of the following statements as true/false Signed-magnitude and two's complement both have two representations for zero. The largest positive unsigned decimal number that can be expressed in six bits is 63 The range of decimal values that can be expressed in seven bits using binary two's complement is -32 to 31. The general idea of Booth's algorithm is to increase the speed of addition when there are consecutive zeroes or ones in the multiplier. Only a limited range of real numbers can be expressed using the IEEE 754 standard. ASCII is a 7-bit code, while Unicode is a 16-bit code.

Explanation / Answer

a) Yes both signed magnitude and two's compliment have two representations of zers the only difference is using two complement one can represent more number using same number of bits.

b) Yes largest unsigned decimal number represented by six bits is 63 ( 2^6-1 which is 64-1 = 63)

c) No the range is -64 to 63 as below

when we talk about two complement that is signed so we will keep 1 bit for sign and  for n bits the largest is 2^n - 1 and the smallest is -2^n

2^(7-1) -1 = 2^6-1 = 63

-2^(7-1) = -2^6 = -64

d) Yes it uses first multiplication and then addition scheme to fast the speed of addition

e) Yes only a range can be represented.

f) Unicode is super set of ASCII code where first 128 numbers are same, ASCII uses 7 bits (2*7 = 128) .

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