ASCII	DECIMAL	HEXADECIMAL	OCTAL	BINARY
null	0	0	0	0
start of header	1	1	1	1
start of text	2	2	2	10
end of text	3	3	3	11
end of transmission	4	4	4	100
enquire	5	5	5	101
acknowledge	6	6	6	110
bell	7	7	7	111
backspace	8	8	10	1000
horizontal tab	9	9	11	1001
linefeed	10	A	12	1010
vertical tab	11	B	13	1011
form feed	12	C	14	1100
carriage return	13	D	15	1101
shift out	14	E	16	1110
shift in	15	F	17	1111
data link escape	16	10	20	10000
device control 1/Xon	17	11	21	10001
device control 2	18	12	22	10010
device control 3/Xoff	19	13	23	10011
device control 4	20	14	24	10100
negative acknowledge	21	15	25	10101
synchronous idle	22	16	26	10110
end of transmission block	23	17	27	10111
cancel	24	18	30	11000
end of medium	25	19	31	11001
end of file/ substitute	26	1A	32	11010
escape	27	1B	33	11011
file separator	28	1C	34	11100
group separator	29	1D	35	11101
record separator	30	1E	36	11110
unit separator	31	1F	37	11111
space	32	20	40	100000
!	33	21	41	100001
	34	22	42	100010
#	35	23	43	100011
$	36	24	44	100100
%	37	25	45	100101
&	38	26	46	100110
‘	39	27	47	100111
(	40	28	50	101000
)	41	29	51	101001
*	42	2A	52	101010
+	43	2B	53	101011
		44	2C	54
–	45	2D	55	101101
.	46	2E	56	101110
/	47	2F	57	101111
0	48	30	60	110000
1	49	31	61	110001
2	50	32	62	110010
3	51	33	63	110011
4	52	34	64	110100
5	53	35	65	110101
6	54	36	66	110110
7	55	37	67	110111
8	56	38	70	111000
9	57	39	71	111001
:	58	3A	72	111010
;	59	3B	73	111011
<	60	3C	74	111100
=	61	3D	75	111101
>	62	3E	76	111110
?	63	3F	77	111111
@	64	40	100	1000000
A	65	41	101	1000001
B	66	42	102	1000010
C	67	43	103	1000011
D	68	44	104	1000100
E	69	45	105	1000101
F	70	46	106	1000110
G	71	47	107	1000111
H	72	48	110	1001000
I	73	49	111	1001001
J	74	4A	112	1001010
K	75	4B	113	1001011
L	76	4C	114	1001100
M	77	4D	115	1001101
N	78	4E	116	1001110
O	79	4F	117	1001111
P	80	50	120	1010000
Q	81	51	121	1010001
R	82	52	122	1010010
S	83	53	123	1010011
T	84	54	124	1010100
U	85	55	125	1010101
V	86	56	126	1010110
W	87	57	127	1010111
X	88	58	130	1011000
Y	89	59	131	1011001
Z	90	5A	132	1011010
[	91	5B	133	1011011
\	92	5C	134	1011100
]	93	5D	135	1011101
^	94	5E	136	1011110
_	95	5F	137	1011111
`	96	60	140	1100000
a	97	61	141	1100001
b	98	62	142	1100010
c	99	63	143	1100011
d	100	64	144	1100100
e	101	65	145	1100101
f	102	66	146	1100110
g	103	67	147	1100111
h	104	68	150	1101000
i	105	69	151	1101001
j	106	6A	152	1101010
k	107	6B	153	1101011
l	108	6C	154	1101100
m	109	6D	155	1101101
n	110	6E	156	1101110
o	111	6F	157	1101111
p	112	70	160	1110000
q	113	71	161	1110001
r	114	72	162	1110010
s	115	73	163	1110011
t	116	74	164	1110100
u	117	75	165	1110101
v	118	76	166	1110110
w	119	77	167	1110111
x	120	78	170	1111000
y	121	79	171	1111001
z	122	7A	172	1111010
{	123	7B	173	1111011
|	124	7C	174	1111100
}	125	7D	175	1111101
~	126	7E	176	1111110
DEL	127	7F	177	1111111
	128	80	200	10000000
	129	81	201	10000001
	130	82	202	10000010
	131	83	203	10000011
	132	84	204	10000100
	133	85	205	10000101
	134	86	206	10000110
	135	87	207	10000111
	136	88	210	10001000
	137	89	211	10001001
	138	8A	212	10001010
	139	8B	213	10001011
	140	8C	214	10001100
	141	8D	215	10001101
	142	8E	216	10001110
	143	8F	217	10001111
	144	90	220	10010000
	145	91	221	10010001
	146	92	222	10010010
	147	93	223	10010011
	148	94	224	10010100
	149	95	225	10010101
	150	96	226	10010110
	151	97	227	10010111
	152	98	230	10011000
	153	99	231	10011001
	154	9A	232	10011010
	155	9B	233	10011011
	156	9C	234	10011100
	157	9D	235	10011101
	158	9E	236	10011110
	159	9F	237	10011111
	160	A0	240	10100000
	161	A1	241	10100001
	162	A2	242	10100010
	163	A3	243	10100011
	164	A4	244	10100100
	165	A5	245	10100101
	166	A6	246	10100110
	167	A7	247	10100111
	168	A8	250	10101000
	169	A9	251	10101001
	170	AA	252	10101010
	171	AB	253	10101011
	172	AC	254	10101100
	173	AD	255	10101101
	174	AE	256	10101110
	175	AF	257	10101111
	176	B0	260	10110000
	177	B1	261	10110001
	178	B2	262	10110010
	179	B3	263	10110011
	180	B4	264	10110100
	181	B5	265	10110101
	182	B6	266	10110110
	183	B7	267	10110111
	184	B8	270	10111000
	185	B9	271	10111001
	186	BA	272	10111010
	187	BB	273	10111011
	188	BC	274	10111100
	189	BD	275	10111101
	190	BE	276	10111110
	191	BF	277	10111111
	192	C0	300	11000000
	193	C1	301	11000001
	194	C2	302	11000010
	195	C3	303	11000011
	196	C4	304	11000100
	197	C5	305	11000101
	198	C6	306	11000110
	199	C7	307	11000111
	200	C8	310	11001000
	201	C9	311	11001001
	202	CA	312	11001010
	203	CB	313	11001011
	204	CC	314	11001100
	205	CD	315	11001101
	206	CE	316	11001110
	207	CF	317	11001111
	208	D0	320	11010000
	209	D1	321	11010001
	210	D2	322	11010010
	211	D3	323	11010011
	212	D4	324	11010100
	213	D5	325	11010101
	214	D6	326	11010110
	215	D7	327	11010111
	216	D8	330	11011000
	217	D9	331	11011001
	218	DA	332	11011010
	219	DB	333	11011011
	220	DC	334	11011100
	221	DD	335	11011101
	222	DE	336	11011110
	223	DF	337	11011111
	224	E0	340	11100000
	225	E1	341	11100001
	226	E2	342	11100010
	227	E3	343	11100011
	228	E4	344	11100100
	229	E5	345	11100101
	230	E6	346	11100110
	231	E7	347	11100111
	232	E8	350	11101000
	233	E9	351	11101001
	234	EA	352	11101010
	235	EB	353	11101011
	236	EC	354	11101100
	237	ED	355	11101101
	238	EE	356	11101110
	239	EF	357	11101111
	240	F0	360	11110000
	241	F1	361	11110001
	242	F2	362	11110010
	243	F3	363	11110011
	244	F4	364	11110100
	245	F5	365	11110101
	246	F6	366	11110110
	247	F7	367	11110111
	248	F8	370	11111000
	249	F9	371	11111001
	250	FA	372	11111010
	251	FB	373	11111011
	252	FC	374	11111100
	253	FD	375	11111101
	254	FE	376	11111110
	255	FF	377	11111111

 

Hex to decimal converter

 

A number system is a collection of values that are used to represent quantities. We talk about the number of students in class, the number of modules each student takes, and we use numbers to symbolize the grades students receive on assessments. We can make sense of our surroundings by quantifying values and items about one another. We do this from a young age, determining whether we have more toys to play with, more presents to open, and more lollipops to eat, and so on.

Throughout history, people have employed signs or symbols to symbolize numbers. Straight lines or groupings of lines were used in the early forms, much like in the movie Robinson Crusoe, where a series of six vertical lines with a diagonal line across indicated one week.

Instructions are supplied in digital systems via electric signals, which are varied by changing the voltage of the signal. It’s tough to establish a decimal number system in digital equipment with ten separate voltages. As a result, numerous digitally implementable number systems have been devised.

You’re undoubtedly already familiar with the concept of a number system—have you heard of binary or hexadecimal numbers? A number system is simply a method of representing numbers. We are accustomed to working with the base-10 number system, generally known as a decimal. Base-16 (hexadecimal), base-8 (octal), and base-2 are some other common number systems (binary).

Hexadecimal:

Binary numbers are an excellent way for computers to represent numbers. They’re not as great for humans though—they’re so very long, and it takes a while to count up all those 111s and 000s. When computer scientists affect numbers, they often use either the decimal numeration system or the hexadecimal number system. Yes, another number system! Fortunately, number systems are more alike than they’re different, and now that you’ve got mastered decimal and binary, hexadecimal will hopefully add up.

Hexadecimal numeration system has 16 digits that range from 0 to 9 and A to F. Its base is 16. The A to F alphabets represents 10 to fifteen decimal numbers. The position of every digit during a hexadecimal number represents a selected power of the bottom (16) of the amount system.

Because the binary number system has only sixteen digits, any hexadecimal number may be converted to a binary number using four bits (24=16). You can call it alphanumeric numeration system as it uses alphabets and numeric digits. Good thing about hex is it uses less memory to store more numbers. These numbers represent computer memory address, conversion from hexadecimal to binary and vice-versa is easier and input and output in hexadecimal form can be handled easily.

The Hexadecimal or Hex, numbering system is widely used in computer and digital systems to convert long strings of binary values into four-digit sets that are easy to grasp. Because this form of digital numbering system includes 16 different numbers from 0-to-9 and A-to-F, the word “Hexadecimal” means “16.”

Hexadecimal describes a base-16 numeral system. The standard numeral system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Hexadecimal uses the decimal numbers and six extra symbols. There are no numerical symbols that represent values greater than nine, so letters taken from the English alphabet are used, specifically A, B, C, D, E and F. Hexadecimal A = decimal 10, and hexadecimal F = decimal 15.

In mathematics and computing, the hexadecimal (also base 16 or hex) is a positional numeral system that represents numbers using a radix (base) of 16.

The hexadecimal system can express negative numbers the same way as in decimal: −2A to represent −42₁₀ and so on.

Hexadecimal can also be used to express the exact bit patterns used in the processor, so a sequence of hexadecimal digits may represent a signed or even a floating point value. This way, the negative number −42₁₀ can be written as FFFF FFD6 in a 32-bit CPU register (in two’s-complement), as C228 0000 in a 32-bit FPU register or C045 0000 0000 0000 in a 64-bit FPU register (in the IEEE floating-point standard).

Similarly as decimal numbers can be addressed in outstanding documentation, so too can hexadecimal numbers. By show, the letter P (or p, for “power”) addresses times two raised to the force of, while E (or e) fills a comparative need in decimal as a feature of the E documentation. The number after the P is decimal and addresses the double example. Expanding the example by 1 increases by 2, not 16. 10.0p1 = 8.0p2 = 4.0p3 = 2.0p4 = 1.0p5. Typically, the number is standardized so the main hexadecimal digit is 1 (except if the worth is by and large 0).

Model: 1.3DEp42 addresses 1.3DE16 × 24210.

Hexadecimal outstanding documentation is needed by the IEEE 754-2008 parallel drifting point standard. This documentation can be utilized for drifting point literals in the C99 release of the C programming language.[22] Using the %a or %A change specifiers, this documentation can be delivered by executions of the printf group of capacities following the C99 specification[23] and Single Unix Specification (IEEE Std 1003.1) POSIX standard.[24]

Why Base 16?

Now, you would possibly be wondering what it’s that computer scientists like such a lot about the hexadecimal number system.

Early computers had 4-bit architectures, which meant that the bits were always processed in groups of four. That’s why we still write bits in groups of 4, like when we write 011101110111 to represent decimal 777 even though we could just write 111111111. The lowest value is 000 (all 000s, 000000000000) and the highest value is 151515 (all 111s, 111111111111), so 4 bits can represent 16 unique values. There’s that number 16!

Hexadecimal numbers are base-16, whereas the decimal numbers that we are familiar with are base-10. (9C36)_16 (using _16 to represent base-16) is equivalent to (39990) _10 (using _10 to represent base-10).

You can determine this result through the subsequent process:

Pick apart each of the hexadecimal number’s digits, starting with the last and working your way up to the first: 6 3 C 9. Remember that the letter ‘C’ stands for the number 12 in hexadecimal, so your answer is 6 3 12 9.

Now, multiply by powers of 16, ranging from 0:

6 * 16^0 = * 1 = 6

3 * 16^1 = 3 * 16 = 48

12 * 16^2 = 12 * 256 = 3072

9 * 16^3 = 9 * 4096 = 36864

Sum of the results – 6 + 48 + 3072 + 36864 = 39990.

This conversion process would hold regardless of how long the hexadecimal number is, just continue multiplying by incremental powers of 16 then sum the results.

Each group of 4 bits in binary may be a single digit within the hexadecimal number system. This makes converting binary numbers to hexadecimal numbers incredibly simple, and it also makes it a very natural computer to operate.

Decimal:

 

In Mathematics, numbers are often classified into differing types, namely real numbers, natural numbers, whole numbers, rational numbers, etc. Decimal numbers are among them. It is the quality representing integer and non-integer numbers. In algebra, a decimal number is often defined as a variety whose integer part and fractional part are separated by a percentage point. The dot during a decimal number is named a percentage point. The digits following the percentage point show a worth smaller than one.

Decimals are supported by the preceding powers of 10. Therefore, as we flow from left to right, the value of digits receives divided through 10, meaning the decimal place value determines the tenths, hundredths, and thousandths. A tenth means one-tenth or 1/10. In decimal form, it is 0.1. Hundredth means 1/100. In decimal form, it is 0.01.

We have learned that decimals are an extension of our numeration system. We also know that decimals are often considered as fractions whose denominators are 10, 100, 1000, etc. The numbers expressed within the decimal form are called decimal numbers or decimals. For example: 6.2, 5.16, 21.69, etc.

 

A decimal number has two parts:

• Whole number part
• Decimal part

A dot separates these parts (.) called the percentage point.

• The digits lying to the left of the percentage point form the entire number part. it begins with ones, tens, hundreds, thousands, and so on.
• The decimal point, together with the digits laying on the right of the decimal point, forms the decimal part. It begins tenths, hundredths, thousandths, and so on.

Decimal notation is the writing of numbers in the base-ten numeral system, which uses various symbols (called digits) for no more than ten distinct values (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) to represent any numbers, no matter how large. These digits are often used with a decimal separator which indicates the start of a fractional part, and with one of the sign symbols + (positive) or − (negative) in front of the numerals to indicate sign.

For composing numbers, the decimal framework utilizes ten decimal digits, a decimal imprint, and, for negative numbers, a less sign “−”. The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;[7] the decimal separator is the dab “.” in numerous countries,[4][8] yet additionally a comma “,” in other countries.[5]

For addressing a non-negative number, a decimal numeral comprises of

either a (limited) arrangement of digits, (for example, “2017”), where the whole succession addresses a number,

or then again a decimal imprint isolating two arrangements of digits, (for example, “20.70828”)

.

On the off chance that m > 0, that is, if the principal grouping contains at any rate two digits, it is for the most part accepted that the primary digit am isn’t zero. In certain conditions it could be helpful to have at least one 0’s on the left; this doesn’t change the worth addressed by the decimal: for instance, 3.14 = 03.14 = 003.14. Additionally, if the last digit on the privilege of the decimal imprint is zero—that is, if bn = 0—it very well might be taken out; on the other hand, following zeros might be added after the decimal imprint without changing the addressed number; [note 1] for instance, 15 = 15.0 = 15.00 and 5.2 = 5.20 = 5.200.

For addressing a negative number, a short sign is set before am.

The numeral  addresses the number.

Decimal fractions (sometimes called decimal numbers, specially in contexts involving explicit fractions) are the rational numbers that may be expressed as a fraction whose denominator is a power of ten.^[9] For example, the decimals 

 represent the fractions 8/10, 1489/100, 24/100000, +1618/1000 and +314159/100000, and are therefore decimal numbers.

More generally, a decimal with n digits after the separator represents the fraction with denominator 10ⁿ, whose numerator is the integer obtained by removing the separator.

It follows that a number is a decimal fraction if and only if it has a finite decimal representation.

Expressed as a fully reduced fraction, the decimal numbers are those whose denominator is a product of a power of 2 and a power of 5. Thus the smallest denominators of decimal numbers are

 

 

 

Converting a Hexadecimal to a Decimal:

 

How do we convert a hex to a decimal? First, you want to know the letters during a hex all have decimal equivalents, as listed within the table below.

 

There is another number system table with more values for octal, hexes, decimals, and binaries; however, the table below provides all that we need to convert hex to dec.

 

Hexadecimal number is one among the amount systems which has value is 16, and it’s only 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F. A, B, C, D, E and F are single bit representations of decimal value 10, 11, 12, 13, 14 and 15. The numeration system |positional notation positional representation system” decimal numeration system is the most familiar number system to the overall public. It is base 10 which have only 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

 

To convert a hexadecimal to a decimal manually, start out by multiplying the hex number by 16. Then, raise it to an influence of 0 and increase that power by 1 whenever consistent with the hexadecimal number equivalent.

We start from the proper of the hexadecimal number and attend the left when applying the powers. Each time you multiply variety by 16, the facility of 16 increases.

 

For some, this may not seem easy at first. But rest assured that with a touch practice, converting from hexadecimal to a decimal is often easily mastered.

 

It may assist you to see your answers employing a calculator or type your decimal value within the dec setting, then select “hex” and press equal. Still, strongly recommend you find out how to convert these number systems manually before using the calculator. That way, you won’t feel that you need to rely on a calculator.

 

 

Rational Numbers

Similarly as with other numeral frameworks, the hexadecimal framework can be utilized to address rational numbers, despite the fact that rehashing extensions are basic since sixteen (1016) has just a solitary prime factor; two.

For any base, 0.1 (or “1/10”) is consistently identical to one separated by the portrayal of that base worth in its own number framework. Hence, regardless of whether isolating one by two for double or separating one by sixteen for hexadecimal, both of these parts are composed as 0.1. Since the radix 16 is an ideal square (42), parts communicated in hexadecimal have an odd period significantly more regularly than decimal ones, and there are no cyclic numbers (other than insignificant single digits).

Repeating digits are shown when the denominator in most reduced terms has a superb factor not found in the radix; subsequently, when utilizing hexadecimal documentation, all divisions with denominators that are not a force of two outcome in a boundless line of repeating digits (like thirds and fifths). This makes hexadecimal (and twofold) less advantageous than decimal for addressing normal numbers since a bigger extent lie outside its scope of limited portrayal.

All judicious numbers limitedly representable in hexadecimal are likewise limitedly representable in decimal, duodecimal and sexagesimal: that is, any hexadecimal number with a limited number of digits additionally has a limited number of digits when communicated in those different bases. Then again, just a small amount of those limitedly representable in the last bases are limitedly representable in hexadecimal. For instance, decimal 0.1 compares to the boundless repeating portrayal 0.19 in hexadecimal. Nonetheless, hexadecimal is more proficient than duodecimal and sexagesimal for addressing portions with forces of two in the denominator. For instance, 0.062510 (one-sixteenth) is comparable to 0.116, 0.0912, and 0;3,4560.

Conclusion:  

 

Every day, we deal with numbers while dealing with money, weight, and length. When greater precision is required than whole numbers can supply, decimal numbers are utilized. When we calculate our weight on the weighing machine, we don’t always get a weight that equals a whole number on the scale. To figure out our exact weight, we need to know what the decimal value on the scale m is.

 

The place value pattern continues in both ways until infinity; places get greater as you move to the left but smaller as you move to the right. We can represent infinitely large and indefinitely small numbers with simple symbols. It’s all part of mathematics’ wonderful order!

 

The fundamental benefit of a Hexadecimal Number is that it is very compact. Because it has a base of 16, the number of digits necessary to express a given number is usually less than in binary or decimal. Converting from hexadecimal and binary numbers is also rapid and simple. Many computer-related professions benefit significantly from understanding several number systems. Binary and hexadecimal are highly prevalent, and I recommend that you learn them thoroughly.