4.1.2 State the mantissa and exponent of a binary number in floating-point representationi. Relate this to scientific notation in decimal.
Teaching Note:
For negative binary numbers in integer and real formats, only the method-of-2's complement is required.
Sample Question:
The number 234.45 base 10 can be represented in the form 0.23445×10^3. The mantissa is
23445 (i.e. the figures after the point) and the exponent is 3 (as the point has been
moved 3 places to the left). The “10” represents base 10.
Now consider the number 3.75 base 10 = 11.11 base 2.
The number 11.11 base 2 would be represented as 0.1111×2^10. The mantissa is 1111 base 2 (i.e. the
figures after the point) and the exponent is base 10 2 (as the point has moved base 10 2 places to
the left). The “2” represents base 2.
(e) State the mantissa and the exponent for the binary equivalent of the number 4.5 base 10
calculated in part (d) above. [2 marks]
(f) Calculate the value of the number represented by a mantissa of 1101 base 2 and an
exponent of 11 base 2 , and then convert it to base 10. [2 marks]
JSR Notes:
For JSR Teaching Notes, see 4.1.3 --> 4.1.2 and 4.1.3 work best when they are explained together.