NUMBER SYSTEMS AND OPERATIONS

     

       Arithmetics for Computers (Number Systems and Operations)

        The table below shows the number when in decimal, binary and hexadecimal.

                   

                    Numeral systems conversion table

        DECIMAL                                BINARY                                  HEXADECIMAL

                  0                                0000                                       0

               1                                0001                                       1

               2                                0010                                       2

               3                                0011                                       3

               4                                0100                                       4

               5                                0101                                       5

               6                                0110                                       6

               7                                0111                                       7

               8                                1000                                       8

               9                                1001                                       9

               10                               1010                                       A

               11                               1011                                       B

               12                               1100                                       C

               13                               1101                                       D

               14                               1110                                       E

               15                               1111                                       F

How to convert from binary to decimal 

Convert binary 110011.11  to decimal:

 The decimal number is equal to the sum of powers of 2 of the binary number's '1' digits place:

1	1	0	0	1	1	.	1	1
1^5	1^4	0^3	0^2	1^1	1^0	.	1^-1	1^-2

=  (1x1^5 )+(1x1^4 )+( 1x1^1)+(1x1^0).(1x1^-1 )+(1x1^-2)

= 51.75  #

How to convert from hex to binary

Convert each 4 binary digits to hex digit  according to this table:

Bin:	0000	0001	0010	0011	0100	0101	0110	0111
Hex:	0	1	2	3	4	5	6	7

 

1000	1001	1010	1011	1100	1101	1110	1111
8	9	A	B	C	D	E	F

 

Example #1

 à Convert (01001110)₂ to hex:

   (0100)₂ = (4)₁₆

   (1110)₂ = (E)₁₆

        _{----------------------------------------}

      (01001110)₂ = (4E)₁₆

Example #2

àConvert (0100101000000001)₂ to hex:

(0100)₂ = (4)₁₆

(1010)₂ = (A)₁₆

(0000)₂ = (0)₁₆

                       + (0001)₂ = (1)₁₆

-----------------------------------------

 (0100101000000001)₂ = (4A01)_{16  #}

How to convert from hex to decimal

Example #1

E7A9 in base 16 is equal to each digit multiplied with its corresponding power of 16:

E7A9₁₆ =

E	7	A	9
14×163	7×162	10×161	9×160
57344	1792	160	9

Total = 59305

                                                                  ~ameerah~

MIPS Basic Instruction Formats

MIPS format instruction.

This three type of format is used to represent instructions which are encoded in binary.

Source :

https://www.google.com/search?hl=en&site=imghp&tbm=isch&source=hp&biw=1366&bih=642&q=MIPS&oq=MIPS&gs_l=img.3..0l10.2891.3594.0.5766.4.4.0.0.0.0.125.484.0j4.4.0....0...1ac.1.32.img..0.4.484.o2kdfDvHnt0#hl=en&q=MIPS+I-FORMAT+instruction&tbm=isch&facrc=_&imgdii=_&imgrc=XFaDLd8TNYg04M%3A%3BwtofKZ7PNfV3yM%3Bhttp%253A%252F%252Fwww.cise.ufl.edu%252F~mssz%252FCompOrg%252FFigure2.7-MIPSinstrFmt.gif%3Bhttp%253A%252F%252Fwww.cise.ufl.edu%252F~mssz%252FCompOrg%252FCDA-lang.html%3B521%3B318

-Ameerah-

Language of the Computer : Part 2 :D

Part 2 yaww..

In MIPS, it has its own register convention. Yeah because it has to convert the assembly language into machine language. So, the image below show you the MIPS Register Convention :

Register Operands

MIPS has a 32 x 32-bit register file :

- Use for frequently accessed data.

- Numbered O to 31.

- 32-bit data are called a "word".

Assembler names:

- $tO, $t1....$t9  are for temporary values.

- $s0, $s1,...$s7 are for saved variable.

Language of the Computer

Language is EVERYTHING! Eventhough we couldn't speak but we still can communicate by using body language. So, computer also has it own language. It is called as MIPS. Do you know what MIPS stand for?? MIPS or Microprocessor without Interlocked Pipeline Stages is a reduced instruction set computer ( RISC ) instruction set architecture.

Figure : MIPS R2000 Architecture

The simulator of MIPS is called SPIM. 

The function of SPIM is :

1) Read MIPS assembly language file and translate to machine language.

2) Execute the machine language instructions.

3) Shows content of registers and memory.

4) Works as a debugger.

5) Provides basic OS-like services.

to be continue.............

Source :

- https://www.google.com/search?hl=en&site=imghp&tbm=isch&source=hp&biw=1366&bih=642&q=MIPS&oq=MIPS&gs_l=img.3..0l10.2891.3594.0.5766.4.4.0.0.0.0.125.484.0j4.4.0....0...1ac.1.32.img..0.4.484.o2kdfDvHnt0#hl=en&q=mips+r2000&tbm=isch&facrc=_&imgdii=_&imgrc=a5m77dEKDJsM5M%3A%3B2q_xdamBXQTeXM%3Bhttp%253A%252F%252Fwww.dsi.unive.it%252F~arch%252Fwinspim%252Fspim_manual_mirror%252F_13973_figure268.gif%3Bhttp%253A%252F%252Fwww.dsi.unive.it%252F~arch%252Fwinspim%252Fspim_manual_mirror%252Fnode2.html%3B477%3B536

- https://www.google.com/search?hl=en&site=imghp&tbm=isch&source=hp&biw=1366&bih=642&q=MIPS&oq=MIPS&gs_l=img.3..0l10.2891.3594.0.5766.4.4.0.0.0.0.125.484.0j4.4.0....0...1ac.1.32.img..0.4.484.o2kdfDvHnt0#hl=en&q=mips+register+conventions&tbm=isch&facrc=_&imgdii=_&imgrc=Db4sVxEDOAEJ6M%3A%3BwtofKZ7PNfV3yM%3Bhttp%253A%252F%252Fwww.cise.ufl.edu%252F~mssz%252FCompOrg%252FTable2.1-MIPSregisters.gif%3Bhttp%253A%252F%252Fwww.cise.ufl.edu%252F~mssz%252FCompOrg%252FCDA-lang.html%3B527%3B297

-Nik Iffah-

DIGITAL LOGIC SIMULATOR

 

hope this words can help you..=)

Hye there! For this entry we will learn about multimedia logic. In this topic, we can draw our own logic design and stimulate the circuit also known as 'drag and drop logic design software'. In order to draw the logic design,we must download the software from the Internet ( for example, CEDAR Logic Simulator). 

In the software, we gonna make use of the truth table and K-Maps(so, it's IMPORTANT for you to understand those two topic earlier). So, we have prepared videos related to the logic design based on their types of logic gates (AND gate, OR gate, NOT gate, NAND gate, NOR gate and XOR gate).

XOR gate

OR gate

NAND and NOR gate

AND gate

if you have any question,do not hesitate to ask in comment. Bye !





Source:
http://www.youtube.com/watch?v=KSdcqRn_61w
http://www.youtube.com/watch?v=_c9fQa9qNiE
http://www.youtube.com/watch?v=JaZrrDAkB5s

- Aliah Razak -

Karnaugh Map

So, in order to change the world we have to be crazy. Haha.

Okay, let's get back to our topic. In this entry, we are going to make you really seriously understand about Karnaugh Maps. Karnaugh Maps or K-Maps is an easy method of simplifying Boolean expressions. K-Maps work effectively to expressions of more than two variables. 

This is a video which show you on how to imply the K-Maps in different number of variables :

Thank you for lending us your eyes and good luck ! 

Source:

http://www.youtube.com/watch?v=b4JiIknHm1Y

- sofea zaini -

Laws of Boolean Algebra

Bonjour people ! Now, we are going to fill up your mind about The Laws of Boolean Algebra. Did you guys know what is Boolean Algebra?? It is definitely NOT the same as Algebraic Expressions. It is totally different thing. Laws of Boolean Algebra is one of the ways to simplify Boolean Equation ( which we already explained it to you at the previous post ). Boolean Algebra is well-known as Boolean Expresions. It can be simplified or manipulated. But to do that, we must follow a certain rules, which is:

Basic Laws of Boolean Algebra

Source :

https://www.google.com/search?q=law+of+boolean+algebra&newwindow=1&source=lnms&tbm=isch&sa=X&ei=iKmdUvm1McmHrQeQ14C4Dg&ved=0CAkQ_AUoAQ&biw=1366&bih=642#facrc=_&imgdii=_&imgrc=R6OcDxOvkm1bbM%3A%3BG4XBP8V1EZ0PUM%3Bhttp%253A%252F%252Fimg688.ph.126.net%252F8GRK63AXmJfFNCJR0np7PA%253D%253D%252F1161647228886098699.gif%3Bhttp%253A%252F%252Fconstforce.blog.163.com%252Fblog%252Fstatic%252F163881235201011212351623%252F%3B500%3B294

- sofea zaini -