The round-off error is independent of the type of fixed point representation. The maximum error that can be introduced through rounding is 0.5(2-b+2-bm) and this can be either positive or negative, depending on the value of x. Therefore, the round-off error is symmetric about zero and falls in the range

According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).

The ones complement of (1100)2 is (0011)2. Thus the two complement of this number is obtained as (0011)2+(0001)2=(0100)2.

Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.

The number (-3/8) is stored in the computer as the 2’s complement of (3/8)

(101.01)2=1*22+0*21+1*20+0*2-1+1*2-2=(5.25)10

For a two’s complement representation, the truncation error is always negative and falls in the range

According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).

According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).

A fixed point representation of numbers allows us to cover a range of numbers, say, xmax-xmin with a resolution