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Number Systems (15)
(a) Represent the integer -5010 in 8 bits in each of the following
three formats:
sign-modulus, one’s complement, and two’s complement. [3]
(b) This question concerns a 12-bit floating-point number format,
consisting of an
8-bit mantissa followed by a 4-bit exponent, both in two’s complement.
(i) What values (in decimal) are represented by the 12-bit patterns
AC716
and 62616? [4]
(ii) Add these two numbers in binary (show your working), and express
the
result in decimal. [4]
(iii) Explain the purpose of normalisation, and normalise your
answer to part
(ii). [2]
(iv) Express in hexadecimal and in decimal the smallest negative value,
that
is the negative value closest to zero, that can be expressed in this
floating-point format. [2]
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