Answers: Floating-Point Binary

Updated 9/30/2002

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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
1  5/8
 1.625
 11.11
 3  3/4
 3.75
 1.1
1 1/2
 1.5
 101.001
5  1/8
 5.125
 1101.0101
13  5/16
 13.3125
 1110.00111
14  7/32
 14.21875
 10000.101011
16  43/64
 16.671875
 111.0000011
7  3/128
 7.0234375
 11.000101
3  5/64
 3.078125

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
10000001
5
10000100
0
01111111
-10
01110101
128
11111111
-1
01111110

 

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 1.000011 4
1101.101 1.101101 3
.00101 1.01 -3
1.0001 1.0001 0
10000011.0 1.0000011 7
.0000011001 1.1001 -6

 

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 1  01111111  11000000000000000000000
 +1101.101 0  10000010  10110100000000000000000
 -.00101 1  01111100  01000000000000000000000
 +100111.0 0  10000100  00111000000000000000000
 +.0000001101011 0  01111000  10101100000000000000000