Question

[10] <§3.5> Write down the bit pattern assuming that we are using base 15 numbers in the fraction instead of base 2. (Base 16 numbers use the symbols 0–9 and A–F. Base 15 numbers would use 0–9 and A–E.) Assume there are 24 bits, and you do not need to normalize. Is this representation exact?

Short answer

The bit pattern is 3D7.EB4.

Yes, the representation is exact.

Step-by-step solution

Define the concept.

The base 15 number system uses the base 15, the symbols 0 to 9, and A to E where the decimal number system uses base 10 and the binary number system uses base 2.

For example,

In the 15 base number system, “A” is equivalent to the value of decimal number system “10” and that is also equivalent to the value of binary number system “1010”,

In the 15 base number system, “B” is equivalent to the value of decimal number system “11” and that is also equivalent to the value of binary number system “1011”,

In the 15 base number system, “C” is equivalent to the value of decimal number system “12” and that is also equivalent to the value of binary number system “1100” ”,

In the 15 base number system, “D” is equivalent to the value of decimal number system “13” and that is also equivalent to the value of binary number system “1101” ”,

In the 15 base number system, “E” is equivalent to the value of decimal number system “14” and that is also equivalent to the value of binary number system “1110”.

In the 15 base number system, “3” is also equivalent to the value of binary number system “0011”.

In the 15 base number system, “7” is also equivalent to the value of binary number system “0111”.

Determine the calculation

The required bit pattern is written below by using the base 15 number system in the fraction and also by assuming there are 24 bits, and without normalization

0011 1101 0111.1110 1011 0100

3D7.EB4 is represented in 24-bit 15 base number system.

$$\begin{gathered} 001111010111111010110100 \\ 3D7EB4 \end{gathered}$$

Yes, the representation is exact.