# Floating-Point Binary Representation

Updated 9/30/2002

1. For each of the following binary floating-point numbers, supply the equivalent value as a base 10 fraction, and then as a base 10 decimal. The first problem has been done for you:

 Binary Floating-Point Base 10 Fraction Base 10 Decimal 1.101 (sample) 1  5/8 1.625 11.11 1.1 101.001 1101.0101 1110.00111 10000.101011 111.0000011 11.000101

2. For each of the following exponent values, shown here in decimal, supply the actual binary bits that would be used for an 8-bit exponent in the IEEE Short Real format. The first answer has been supplied for you:

 Exponent (E) Binary Representation 2 (sample) 10000001 5 0 -10 128 -1

3. For each of the following floating-point binary numbers, supply the normalized value and the resulting exponent. The first answer has been supplied for you:

 Binary Value Normalized As Exponent 10000.11 (sample) 1.000011 4 1101.101 .00101 1.0001 10000011.0 .0000011001

4. For each of the following floating-point binary examples, supply the complete binary representation of the number in IEEE Short Real format. The first answer has been supplied for you:

 Binary Value Sign, Exponent, Mantissa -1.11 (sample) 1  01111111  11000000000000000000000 +1101.101 -.00101 +100111.0 +.0000001101011