I've found such numbers time and time again in verilog and digital logic exercises, but I don't know how I'm supposed to know what number this is or how to write it as 12'b in verilog code.
Can someone explain them to me?
Presumably it's a 12-bit value in hexadecimal notation. Since one hexadecimal digit encodes 4 bits, there are 3 hexadecimal digits:
hexadecimal 0 corresponds to 4 bits 0000
hexadecimal 6 corresponds to 4 bits 0110
hexadecimal f corresponds to 4 bits 1111
So the same value in binary notation is 000001101111.
In Verilog you can write
12'h06f
or
12'b000001101111
Where 12' means "12 bits", h means "hexadecimal" and b means "binary".
The number in the post is known as a literal constant or a number literal or just a literal.
There is a short tutorial document with examples that is a good reference on the subject.
The document can be found here:
https://web.engr.oregonstate.edu/~traylor/ece474/beamer_lectures/verilog_number_literals.pdf
The first page looks like this:
Related
This is surely a duplicate, but I was not able to find an answer to the following question.
Let's consider the decimal integer 14. We can obtain its binary representation, 1110, using e.g. the divide-by-2 method (% represents the modulus operand):
14 % 2 = 0
7 % 2 = 1
3 % 2 = 1
1 % 2 = 1
but how computers convert decimal to binary integers?
The above method would require the computer to perform arithmetic and, as far as I understand, because arithmetic is performed on binary numbers, it seems we would be back dealing with the same issue.
I suppose that any other algorithmic method would suffer the same problem. How do computers convert decimal to binary integers?
Update: Following a discussion with Code-Apprentice (see comments under his answer), here is a reformulation of the question in two cases of interest:
a) How the conversion to binary is performed when the user types integers on a keyboard?
b) Given a mathematical operation in a programming language, say 12 / 3, how does the conversion from decimal to binary is done when running the program, so that the computer can do the arithmetic?
There is only binary
The computer stores all data as binary. It does not convert from decimal to binary since binary is its native language. When the computer displays a number it will convert from the binary representation to any base, which by default is decimal.
A key concept to understand here is the difference between the computers internal storage and the representation as characters on your monitor. If you want to display a number as binary, you can write an algorithm in code to do the exact steps that you performed by hand. You then print out the characters 1 and 0 as calculated by the algorithm.
Indeed, like you mention in one of you comments, if compiler has a small look-up table to associate decimal integers to binary integers then it can be done with simple binary multiplications and additions.
Look-up table has to contain binary associations for single decimal digits and decimal ten, hundred, thousand, etc.
Decimal 14 can be transformed to binary by multipltying binary 1 by binary 10 and added binary 4.
Decimal 149 would be binary 1 multiplied by binary 100, added to binary 4 multiplied by binary 10 and added binary 9 at the end.
Decimal are misunderstood in a program
let's take an example from c language
int x = 14;
here 14 is not decimal its two characters 1 and 4 which are written together to be 14
we know that characters are just representation for some binary value
1 for 00110001
4 for 00110100
full ascii table for characters can be seen here
so 14 in charcter form actually written as binary 00110001 00110100
00110001 00110100 => this binary is made to look as 14 on computer screen (so we think it as decimal)
we know number 14 evntually should become 14 = 1110
or we can pad it with zero to be
14 = 00001110
for this to happen computer/processor only need to do binary to binary conversion i.e.
00110001 00110100 to 00001110
and we are all set
this is a school assignment. I've been given homework and one of the problems is to figure out the value after adding two hexadecimal values.
0x80000000 and 0xD0000000. I understand that D = 13, but I don't understand how the answer is 15, because 8 + 13 = 23? Could someone explain what I am doing wrong, and what I should do instead?
Thanks!
It's easy if you think that every digit represents a quadruple, for example
0xDEADBEEF = 13*16⁷+14*16⁶+10*16⁵+13*16⁴+11*16³+14*16²+14*16¹+15*16⁰.
The above hexadecimal value needs an algorithm to translate to a format the the ALU can add, for instance binary numbers.
D is 13 in decimal because D is digit number 13 if A replaces 10 and so on (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F). The position of D is 7, so the number is 13*16⁷.
We notice that it is easier to LSB if we do this, and recognize that F is 15 in hexadecimal notation and therefore the number to the left will be 15*16⁰=15.
0xFF therefore means 15*16¹+15*16⁰=15*16+15=255 (you can check this with a calculator).
Now the algorithm is hopefully clear.
3735928559 is the decimal value of DEADBEEF because ==13*16^7+14*16^6+10*16^5+13*16^4+11*16^3+14*16^2+14*16^1+15*16^0=3735928559.
Some times I convert the hexadecimal into binary base 2 this because I feel more confident to do arithmetic with binary base 2than hexadecimal.
In order to do so you need to arrange every hexadecimal into group of 4 bits binary number.
hex 0x8 + 0xD
Convert to binary
binary 1000 + 1101 = 10101 = 21
group it again as 4 bits
0001 0101 = 0x15
I ignored if it's signed number and didn't used two's complement.
For example: octal 3 is 011 in the binary digits, and decimal 3 is 0011.
So, is there any way to figure them out or this table must be copied and pasted in my memory?
"A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward."
Should we consider 2015 in binary format (111 1101 1111) a palindrome? This is feasible if we can neglect the leftmost 0, but can we do that? I mean in binary each four bits correspond to a decimal digit so we must have a leftmost zero which makes 2015 = 2000+0+10+5 = 0111 1101 0000+0000+1010+0101 = 0111 1101 1111 so can it be considered a palindrome? I know this can seem a dump theoretical question but I want to know the answer. Thanks in advance
11111011111 binary is 2015 decimal, and adding 0's to the left doesn't change its value. Note that you also mentioned: "in binary each four bits corresponds to a decimal digit". That's not the case. Here's an example of how binary corresponds to decimal:
So yes, you can neglect the leftmost 0. And 2015 is a palindrome.
My instructor stated that "an octal byte consists of 6 bits". I am having difficulty understanding why this is, as an octal digit consists of 3 binary bits. I also do not understand the significance of an octal byte being defined as '6 bits' as opposed to some other number.
Can anyone explain why this is, if it is in fact true, or point me to a useful explanation?
This is all speculation and guesswork, since none of this is in any way standard terminology.
An 8-bit byte can be written as two digits of hexadecimals, because each digit expresses 4 bits. The largest such byte value is 0xFF.
By analogy, two digits of octals can express 2 × 3 = 6 bits. Its largest value is 077. So if you like you can call a pair of two octals an "octal byte", but only if you will also call an 8-bit byte a "hexadecimal byte".
In my personal opinion neither notion is helpful or useful, and you'd be best of just to say how many bits your byte has.
Like #Kerrek SB I'd have to guess the same.
Tell him an octal byte is two octal nibbles, that should sort him out.
Two hexadecimal digits is an 8 bit byte, so each four bits were called a nibble.
as for wiki : The byte is a unit of digital information that most commonly consists of 8 bits. The bit is a contraction of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either "1" or "0".
so byte is a set of bunch of bits. to be specific of 8 bits.
we see that the definition doesnt say anything about dec oct hex and other notations of integer number.
indeed byte and integer number is not the same. so where
does it start ?
if we type bits of byte like so 01001010 we can find that
we can map 1-to-1 this object to binary notation
of integer numbers 01001010.
(byte)01001010 --> (binary integer) 01001010
the two objects look the same but actually is just mapping.
now we work with integer number instead of abstract object "byte". an integer
number can be designated via different notations like : dec, binary, hex, oct etc.
notation like octal(hex,dec etc) is just a method of designation of integer number. it does not influence the nature of initial byte object.
byte has 8 bits whatever notation is used.
ISO/IEC 2382-1:1993 says:
1.The number of bits in a byte is usually 8.
2.Octet is Byte that consists of eight
Bits