More Floating Point exam questions

Important to remember is that the decimal point must be between a 0 and a 1. 0.1 or 1.0.

Q1) Using a 7-bit mantissa and a 5-bit exponent using 2's complement format write the smallest number that can be represented:
1.000000    10000

b) Work out what the denary number 416 would be as a binary floating point number with a 7-bit mantissa and a 5-bit exponent.
011010000.0=416
0.1101000         01001

c)1.001110        00100
e) Type of error.
 If two large numbers are multiplied together- This will create an overflow.
If a small number is divided by a large number- this will create an underflow

Q2) A floating point number uses a 8-bit mantissa and a 4-bit exponent.
In binary, write the largest positive number that can be represented using this normalised floating point system.
0.1000000  1000

b) Calculate the denary number of this floating point number.
1.0101000     0011 = -5.5

c) Write the normalised floating point representation of the denary value 13.625 in the boxes below.
01101.101
0.1101101       0100

d) Write the normalised floating point number of the denary value 0.34375 in the boxes below.
0.1011000 1111

e)Explain what overflow is and give an example of a situation which might cause overflow to occur?
When there is a number that is too big to be represented using given number of bits.

Q3) a) The binary pattern 1001 1000 0100 can be interpreted in a number of different ways?
Hexadecimal- BCD
Decimal- 9  8  4