Answers to Exercises

Answers to Exercises Chapter 1 1. :
The internal mechanism of a digital computer can simply be denoted as a
black box which is shown in Figure 1.1. From Figure 1.1, a digital computer
can be thought of as a data processor. A digital program also can be
thought of as a set of instructions written in a digital computer language
that indicates the data processor what to do with the input data. The
output data depend on the combination of two factors: the input data and
the digital program. With the same digital program, you can produce
different outputs if you change the input. Similarly, with the same input
data, you can generate different outputs if you change the digital program.
A digital program
Input Data Output Data
Figure 1.1: Computational model of a digital computer. 2. :
The internal mechanism of bio-molecular computer can simply be defined as
another black box which is shown in Figure 1.2, where some robotics or
electronic computing is used to carry out automatically the majority of the
operations with the test tubes without the intervention of the user. From
Figure 1.2, input data can be encoded in test tubes. Each encoded data in
test tubes can be thought of a data processor. A bio-molecular program also
can be thought of as a set of biological operations written in a high-level
natural language that tells each data processor what to do. The output data
also are based on the combination of two factors: the input data and the
bio-molecular program. With the same bio-molecular program, you can produce
different outputs if you change the input. Similarly, with the same input
data, you can generate different outputs if you change the bio-molecular
program. Finally, if the input data and the bio-molecular program remain
the same, the output should be the same.
A bio-molecular program
Input data in a tube
Output data in a tube
[pic] ... [pic] [pic]
Figure 1.2: Some robotics or electronic computing in an advanced
computational model of bio-molecular computer carries out automatically the
majority of the operations with the test tubes without the intervention of
the user. 3. :
A digital program in a digital computer can be thought of as a set of
instructions written in a digital computer language that indicates the data
processor what to do with the input data. A bio-molecular program in bio-
molecular computer can be thought of as a set of biological operations
written in a high-level natural language that tells each data processor
what to do. 4. :
Memory is the main storage area in the inside of a digital computer. It
is used to store data and digital programs during processing. This implies
that both the data and programs should have the same format because they
are stored in memory. They are, in fact, stored as binary patterns (a
sequence of 0s and 1s) in memory.
Tubes in bio-molecular computer are devices in which input data and
output data are stored and each biological operation is completed. The
function of tubes in bio-molecular computer are actually the same that of
memory and input/output devices in a digital computer. 5. :
An input/output subsystem in a digital computer is an auxiliary storage
area and is also the communication between the digital computer and the
outside world. Inputs are data received by a digital computer, and outputs
are data sent from it. For instance, a keyboard, or a mouse is an input
device for a computer, while a monitor or a printer is an output device for
the computer. A hard disk or a tape is simultaneously input and output
devices.
Input data that are encoded are stored in tubes in bio-molecular
computer. Output data that are produced by a bio-molecular program are also
stored in tubes. Tubes are the only storage device in bio-molecular
computer. 6. :
A bit is the smallest unit of data that can be stored in a digital
computer and bio-molecular computer; it is either 0 or 1. To a digital
computer, bit 0 is encoded by the off state of a switch and bit 1 is
encoded by the on state of the switch. For bio-molecular computer,
different sequences of bio-molecules encode, respectively, bit 0 and bit 1.
7. :
The so-called von Neumann architecture is a model for a computing machine
that uses a single storage structure to hold both the set of instructions
on how to perform the computation and the data required or generated by the
computation. A digital computer system of the von Neumann architecture is
shown in Figure 1.3.
From Figure 1.3, the input subsystem accepts input data and the digital
program from outside the digital computer and the output subsystem sends
the result of processing to the outside. Memory is the main storage area in
the inside of the digital computer system. The arithmetic logic unit is the
core of the digital computer system and is applied to perform calculation
and logical operations. The control unit is employed to control the
operations of the memory, ALU, and the input/output subsystem.
A digital program in the von Neumann architecture is made of a finite
number of instructions. In the architecture, the control unit fetches one
instruction from memory, interprets it, and then excites it. In other
words, the instructions in the digital program are executed one after
another. Of course, one instruction may request the control unit to jump to
some previous or following one instruction, but this does not mean that the
instructions are not executed sequentially. A Digital Program Input Data Output Data
Figure 1.3: A digital computer system of the von Neumann architecture has
four subsystems. 1.8:
In bio-molecular computer, data also are represented as binary patterns
(a sequence of 0s and 1s). Those binary patterns are encoded by sequences
of bio-molecules and are stored in a tube. This is to say that a tube is
the only storage area in bio-molecular computer and is also the memory and
the input/output subsystem of the von Neumann architecture. Bio-molecular
programs are made of a set of bio-molecular operations and are used to
perform calculation and logical operations. So, bio-molecular programs can
be regarded as the arithmetic logic unit of the von Neumann architecture. A
robot is used to automatically control the operations of a tube (the memory
and the input/output subsystem) and bio-molecular programs (the ALU). This
implies that the robot can be regarded as the control unit of the von
Neumann architecture.
In Figure 1.4, bio-molecular computer of the von Neumann architecture is
shown. From Figure 1.4, a robot fetches one bio-molecular operation from a
bio-molecular program (the ALU), and then carries out the bio-molecular
operation for those data stored in the tube (the memory). In other words,
the bio-molecular operations are executed one after another. Certainly, one
bio-molecular operation perhaps requests the robot to perform some previous
or following bio-molecular operations. [pic]
(Control Unit) Figure 1.4: The bio-molecular computer of the von Neumann architecture. Chapter 2 2.1:
(a) In a digital computer, the on state and the off state of a switch
subsequently encode the values 1 and 0 of a bit.
(b) In bio-molecular computer, different sequences of bio-molecules encode
the values 1 and 0 of a bit. This indicates that two different
sequences of bio-molecules can be regarded as the on state and the off
state of a switch in a digital computer, where the on state is regarded
as 1 and the off state is regarded as 0. 2.2:
(a) In a digital computer, a bit pattern that is a string of bits is also
a combination of 0s and 1s. The values 1 and 0 of each bit in a bit
pattern are encoded by the on state and the off state of a switch.
(b) In bio-molecular computer, a bit pattern is a combination of 0s and
1s. If a bit pattern that is made of n bits can be stored in a tube in
bio-molecular computer, then (2 ( n) different sequences of bio-
molecules are needed. 2.3: We would like to give many thanks to Louie Lu who wrote the following
C programs. #include
#define MAX_LEN 100
char * hexadecimal-number-to-its-corresponding-binary-number(char *s)
{ int i, c, dec = 0, dec_tmp;
static char b[MAX_LEN];
while ((c = *s++) != NULL)
{ dec = dec * 16 + (isdigit(c) ? c - '0' : c - 'A' + 10); }
i = 0;
dec_tmp = dec;
while (dec_tmp)
{ i++;
dec_tmp /= 2;
}
while (dec)
{ b[--i] = dec % 2 + '0';
dec /= 2;
}
return b;
} int main()
{ char s[MAX_LEN];
printf("Please input a hexadecimal number: ");
scanf("%s", s);
printf("The corresponding binary number is: %s", hexadecimal-number-to-
its-corresponding-binary-number (s));
} 2.4: We would like to give many thanks to Louie Lu who wrote the following
C programs. #include
#define MAX_LEN 100
char * binary-number-to-its-corresponding-hexadecimal-number(char *s)
{ int c, j, i=0, dec=0;
static char h[MAX_LEN];
static char hex[] = {"0123456789ABCDEF"};
while ((c = *s++) != NULL)
{ dec