This is an arbitrary-precision binary calculator. Let us look at Multiplication, Addition, subtraction & inversion Shift the mantissa of the lesser number by bits Considering the hidden bits. This is a decimal to binary floating-point converter. (And on Chrome it looks a bit ugly because the input boxes are a too wide.) X3= X1 * X2 = 1509.3203125 It displays the the results of the intermediate steps in addition and subtraction. IEEE 754 floating point standard. Lets inverse the above process and convert back the floating point word obtained above to decimal. Add the exponent value after normalization to the biased exponent obtained in step 2. If signs of X1 and X2 are equal (S1 == S2) then add the mantissas the number to the left will be updated. The code doesn't distinguish between quiet and signaling NaN, i.e. Online IEEE 754 floating point converter and analysis. Are you sure you want to create this branch? The rounding mode used is round to nearest, ties to even. Hex result * and,or,not,xor operations are limited to 32 bits numbers . Floating Point Add/Subtract. lowp criteria fulfilled I wrote this converter from scratch it does not rely on native conversion functions like strtod() or strtof() or printf(). It requires exponent width and auto considers the floating point bitwidth. Zigbee If Overflow set the output to infinity & for underflow set to zero. We had to shift the binary points left 8 times to normalize it; exponent value (8) should be added with bias. It is implemented with arbitrary-precision arithmetic, so its conversions are correctly rounded. (And on Chrome it looks B = 0.5625 The IEEE standard defines various binary and decimal formats. Then we would have subtracted the mantissas. 136+1 = 137 => exponent value. Equivalent floating point binary words are, 1) S3 = S1 xor S2 = 0 Binary Numbers, Binary Code, and Binary Logic. So, exponent c = a + b = 0 + 2 = 2 is the resulting exponent. It displays the the results of the intermediate steps in addition and subtraction. Converts to this binary floating-point number (selected forms shown): Correct Decimal To Floating-Point Using Big Integers, Decimal Precision of Binary Floating-Point Numbers, 17 Digits Gets You There, Once Youve Found Your Way, The Spacing of Binary Floating-Point Numbers, Jetpack Compose Byte Converter App: 2022 Version, Anomalies In IntelliJ Kotlin Floating-Point Literal Inspection. The Decimal value of a normalized floating point numbers in IEEE 754 standard is represented as. Let's try to understand the Multiplication algorithm with the help of an example. 2) The binary number is not normalized, Normalize the binary number. mediump criteria fulfilled Copyright (c) 2016, Prof. Dr. Edmund Weitz. The program will then calculate the decimal value matching the input. There are ten output forms to choose from: (See here for more details on these output forms.). satellite 2. Calculator that simulates floating-point numbers at the specified precision Mediump float calculator i.e. Prepend leading 1 to form the mantissa. A function f doing task A is denoted with A@f, This function computes the addition of two floating point numbers given ashex numbers like 0xABCD/0xabcd. number's bit pattern on the right. It can add, subtract, multiply, or divide two binary numbers. IEEE-754 Mantissa: 01000011100011001100110. 0, point, 101, 0.101 x 2, to the power 4 , 2 4.Here, the mantissa is 0, point, 101, 0.101 and the exponent is 4, 4.By definition, the number base of a binary number is always 2, 2.. You may recognise this way of representing numbers as . Subnormal numbers are flushed to zero. = (-1)s1 (M1 x 2E1) * (-1) s2 (M2 x 2E2) 2) We assume that X1 has the larger absolute value of the 2 numbers. The same are given below, 0 11111111 00000000000000000000000 = +INF. Number as Big Endian Single Precision Float: 0x4421C666. Round result. Shift the decimal point such that we get a 1 at the very end (i.e 1.m form). E = 8 + 127 = 135(10) , convert this to binary and we have our exponent value X2=16.9375 The result should be stored in order . 3) Find exponent of the result. The integral portion is the part of the number before the decimal point. You don't need a Ph.D. to convert to floating-point. The result of this division should be all of the remainders that were gathered until you get to a number that cannot be divided by 2. The conversion to binary is explained first because it shows and explains all parts of a binary floating point number step by step. = (-1) S3(M1/M2) 2 (E1-E2), 1) If divisor X2 = zero then set the result to "infinity", if both X1 and X2 are zero's set it to "NAN" and IEEE 754 floating point number to decimal conversion, this will make X3 = (X1/X2) but you can use the buttons below to switch to some of the other variants. python3 FLP.py -ds -a -ew 5 -fa 0x0000 -fb 0x0000, This switch displays rich information about the process including what the inputs-outputs are, what switches are taken into consideration and their values. You signed in with another tab or window. Base Convert. many interesting examples on this course can be demonstrated on a calculatorthe underlying problem is oating point computation and nave-programmer failure to understand it rather than programming per se. First number. A tag already exists with the provided branch name. Hexadecimal Numbers: Uppercase or Lowercase? Enter a positive or negative number, either in standard (e.g., 134.45) or exponent (e.g., 1.3445e2) form. i.e. that the red digit is the hidden bit and can't be changed directly.). Extract the sign of the result from the two sign bits. If your program is printing 0.1, it is lying to you; if it is printing 0.100000001, its still lying, but at least its telling you you really dont have 0.1. It is based on the big integer based algorithm I describe in my article Correct Decimal To Floating-Point Using Big Integers. python FLP.py --add --exponentWidth 5 --floata 0x0600 --floatb 0x0080, The same addition function when given 'sign as 1' computes the difference of two floating point numbers. 6) Check for underflow/overflow. rather just tries to comply to the OpenGL ES shading language spec. 4) Shift the mantissa M2 by (E1-E2) so that the exponents are same for both numbers. 2) Conversion from decimal to floating point (N,E) and vice versa. all NaNs are quiet and use the same bit pattern. If M3 (48) = "1" then left shift the binary point and add "1" floating point word, since it takes up an extra bit location and it Both single and double floating numbers are supported. It is mainly written to verify the result produced by the hardware implementation of floating point unit. All these functionality can be invoked from command line by turing on appropriate switches. It simply consider all ones as NaN. It will convert a decimal number to its nearest single-precision and double-precision IEEE 754 binary floating-point number, using round-half-to-even rounding (the default IEEE rounding mode). for example 42, 2.345, 12E-3, and so on; you can input the values NaN, Inf, and -Inf directly; and you can also enter fractions using the syntax 17/23. This page implements a crude simulation of how floating-point calculations could be performed on a chip implementing n-bit floating point arithmetic. Once you've pressed Enter, = 133-131+127 => 129 => (10000001) The resulting floating-point number can be displayed in ten forms: in decimal, in binary, in normalized decimal scientific notation, in normalized binary scientific notation, as a normalized decimal times a power of two, as a decimal integer times a power of two, as a decimal integer times a power of ten, as a hexadecimal floating-point constant, in raw binary, and in raw hexadecimal. 2) Result of Initial exponent E3 = E1 = 10000010 = 130(10) Inside the computer, most numbers with a decimal point can only be approximated; another number, just a tiny bit away from the one you want, must stand in for it. For example, in single-precision floating-point, 0.1 becomes 0.100000001490116119384765625. algorithms performed on This Tutorial attempts to provide a brief overview of IEEE Floating point Numbers format with the help of simple examples, without going too much into mathematical detail and notations. Floating Point Multiplication is simpler when compared to floating point addition we will discuss the basic floating point multiplication algorithm. Mantissa (M1) =0101_0000_0000_0000_0000_000. zero, X1=127.03125 Add the exponent Binary Calculator. Floating Point Multiplication is simpler when compared to floating point addition. It is implemented in JavaScript and should work with recent desktop versions of Chrome and Firefox . 6. (Note Add mantissas. Floating Point Calculator / Ben Aubin | Observable Ben Aubin benaubin.com CS Student at UT Austin Published Edited Jul 2 CC BY 4.0 2 forks 13 Like s 2 leading_bit = kind == SUBNORMAL ? 4) Calculate the exponent's difference i.e. 6) Check for overflow/underflow python FLP.py -ew 5 -n 16 -d2f 1E-7. Ive implemented it using BCMath. NOTE: For floating point Subtraction, invert the sign bit of the number to be subtracted - FloatingPoint_Calculator/README.md at ma. For more information, see = 133 + 130 - 127 + 1 = 137. (For the record though, this converter accepts all the hard examples Ive discussed on my site.) WebGL getShaderPrecisionFormat would return: the Wikipedia article on the half-precision floating point format. 7. IEEE-754 Floating-Point Conversion from 32-bit Hexadecimal to Floating-Point Enter the 32-bit hexadecimal representation of a floating-point number here, then click the Compute button. Sign bit (S1) =0. (Only scientific calculator can be used.) For all inputs that are accepted however, the output is correct (notwithstanding any bugs escaping my extensive testing). Sign bit = > (0 xor 0) => 0 1) Computing addition/subtraction on N-bit floating point numbers with E-bit exponent. mantissa as shown in the figure below. on a chip implementing n-bit floating point arithmetic. 4) Exponent E3 = (E1 - E2) + bias E1, E2: =>Exponent bits of number X1 & X2. We need to find the Sign, exponent and mantissa bits. A = 9.75 The purpose of this challenge is to write a Python program that will receive, as an input, a binary number expressed using a normalised floating point representation (using a 5-bit mantissa and a 3-bit exponent). Compare exponents. =E1+E2-bias 5) Normalize the sum, either shifting right and incrementing the exponent or shifting left and decrementing the exponent. A: B: hex dec. add sub. Easy-to-use calculator that will help every moonshine. single double It is implemented with arbitrary-precision arithmetic, so its conversions are correctly rounded. Finally, you can use as input bit patterns as shown on the right (the ones starting with 0b or 0x). starting with + or-. Suppose you want to multiply following two numbers: Now, these are steps according to above algorithm: Given, A = 1.11 x 2^0 and B = 1.01 x 2^2. Bias = 2(8-1) - 1 = 127 on the left and press the Enter key, you will see the If(E3 < Emin) then it's a underflow and the output should be set to zero. 5) Normalize if required, i.e by left shifting the mantissa and decrementing the resultant exponent. We need to normalize 10.0011 to 1.00011 and adjust exponent 1 by 3 appropriately. X3 = (M1 x 2E1) +/- (M2 x 2E2). 5. fractions: 3.14. For single precision floating point representation, these patterns are given below, 0 00000000 00000000000000000000000 = +0. 5) Sign bits of both are equal? It doesn't require any specification on the number of bits the floating point has i.e 32,16 bit. X2 = 12.0625 (base 10) So you ve successfully built your own copper still. GLSL precision: Abs(X1) > Abs(X2). to the mantissa of a floating point word for conversions are calculations. Find the absolute value of the exponent difference ( ) and choose the exponent of the greater number. Result X3 = X1 * X2 the Wikipedia article on the half-precision floating point format. i.e. Proofing moonshine is an important part of the process of making it. So we have found mantissa, sign, and exponent bits. Let take a decimal number say 286.75 lets represent it in IEEE floating point format (Single precision, 32 bit). At the end of this tutorial we should be able to know what are floating point numbers and its basic arithmetic operations such as addition, multiplication & division. Impressum, Datenschutzerklrung. 3) The mantissa of the Multiplier (M1) and multiplicand (M2) are multiplied and the result is placed in the resultant field of the mantissa (truncate/round the result for 24 bits). Single Precision Floating Point 1 10110110 11000101100111010110111 Sign Exponent Mantissa 16 -6.384063 x 10 School of Engineering and Computer Science OAKLAND Subtract the two exponents and . --First, divide the number on the left of the decimal point by two while storing the remainder each time. This calculator is, by design, very simple. As example in number 34.890625, the integral part is the number in front of the decimal point (34), the fractional part is the rest after the . 23 = mantissa (m). 1) Represent the Decimal number 286.75(10) into Binary format Now the exponents of both X1 and X2 are same. Note: "1" is hidden in the representation of IEEE 754 LTE An IEEE 754 standard floating point binary word consists of a sign bit, exponent, and a Both single and double floating numbers are supported. Answer: Decimal: Decimal value for IEEE 754 = (-1) S (1+. This converter will show you why numbers in your computer programs, like 0.1, do not behave as youd expect. . Step 6: Convert Both Sides of the Decimal Point Into Binary Numbers. A floating point number has an integral part and a fractional part. Enter a decimal number (e.g., 3.1415, 1.56e-11, 4e20) (no suffixes, commas, operators), (e.g., 0 10000101 11101011000000000000000). S1, S2 => Sign bits of number X1 & X2. As it is generic it can be used for any floating point formats including IEEE-754 format and of any length like FLP64, FLP32, FLP16 etc. to the exponent else don't add anything. 802.11ad 8) If E1 + E2 - bias) is lesser than/equal to Emin then set product to zero. 3. Shift smaller mantissa if necessary. GSM Click Clear to reset the form and start from scratch. 3) Bias =2(e-1) - 1, Note: The normalization of the product is simpler as the range of RADAR, RF Wireless World 2012, RF & Wireless Vendors and Resources, Free HTML5 Templates. wimax In the exponent Yes. Take the number that you would like to convert, and take apart the number so you have a whole number portion and a decimal number portion. Second number = Calculate Reset. The following conversion tool will help you work out the formula used to convert a normalised floating point . It supports Inf, MInf, NaN, denormals and Normal numbers. X1 =, 1) Find the sign bit by xor-ing sign bit of A and B If you want to convert another number, just type over the original number and click Convert there is no need to click Clear first. 3) Divide the mantissas M1/M2, WLAN Decimal to IEEE 754 with Scientific Calculator Steps Question Examples: Question 1: Convert 4.00012 to a 32-bit IEEE 754 single-precision floating-point format, and represent datum of address ADDR+00H to ADDR+03H in big endian. Enter a 64-bit value in hexadecimal and see it analyzed as a single-precision floating-point value. (. Convert the integral portion of the floating-point value to unsigned binary ( not two's complement). 2) E3 = (E1 - E2) + bias = (10000101) - (10000011)+ (1111111) Or you can do it the other way around and manipulate the bits on the right. "1" to the final exponent value. 3) Find mantissa by dividing M1/M2 If signs of X1 and X2 are not equal (S1 != S2) then subtract the mantissas Operation. 00 Inc 10 GST COMBO SPECIAL Buy Any Listed 1000ml Spirit Essence, get ANY 250 ml Spirit Essence FREE 127. This calculator simulates the arithmetic calculations of floating point numbers that are stored in 32-bit format. Binary result. You can see binary, hexadecimal and decimal dump of the number including split into sign, exponent and mantisa parts. This example will use the number 85.125. For practical reasons, Ive set an arbitrary (somewhat) limit on the length of the decimal input; youll get an error message if you hit it. 802.11ac It does not model any specific chip, but rather just tries to comply to the OpenGL ES shading language spec . This function takes in the N+(K>3) bit binary floating point number and returns N-bit number. 0 : 1; significand = Fraction(mantissa, 1n << BigInt(p-1)).add(leading_bit).mul(-2*sign+1); = (-1)S1 (M1 x 2E1) / (-1) S2 (M2 x 2E2) This floating point tutorial covers IEEE 754 Standard Floating Point Numbers,floating point conversions,Decimal to IEEE 754 standard floating point, It is understood that we need to append the "1" You can use it to explore binary numbers in their most basic form. Convert between decimal, binary and hexadecimal Now, multiply 1.11 by 1.01, so result will be 10.0011. 1) Abs (A) > Abs (B)? Objective Floating Point Calculator Addition Subtraction . It is implemented in JavaScript and should work with recent desktop versions of Chrome and Firefox. We got the value of mantissa. Fraction to Binary conversion @FRAC2BIN, Computing addition/subtraction on N-bit floating point numbers with E-bit exponent. X1 = 125.125 (base 10) The default format for this page is binary64, IEEE-754 Floating Point Converter Translations: de This page allows you to convert between the decimal representation of numbers (like "1.02") and the binary format used by all modern CPUs (IEEE 754 floating point). For example, if the number to convert is -0.75, then 0 is the integral portion, and it's unsigned binary . It will convert both normal and subnormal numbers, and will convert numbers that overflow (to infinity) or underflow (to zero). In our case e=8(IEEE 754 format single precision). You can see binary, hexadecimal and decimal dump of the number including split into sign, exponent and mantisa parts. =1. 4) The biased exponent e is represented as If we convert this to decimal we get your floating-point computation results may vary This page implements a crude simulation of how floating-point calculations could be performed on a chip implementing n-bit floating point arithmetic. The major steps for a floating point addition and subtraction are. It returns the bit position where first '1' occurs and fraction value left to compute further bits. your floating-point computation results may vary. Equivalent floating point binary words are Extract exponent and fraction bits. much clear the concept and notations of floating point numbers. I haven't tested with other browsers. It will convert a decimal number to its nearest single-precision and double-precision IEEE 754 binary floating-point number, using round-half-to-even rounding (the default IEEE rounding mode). 48bits (2 bits are to the left of binary point). The subtracted result is put in the exponential field of the result block. Floating Point Calculator Dylan Powell Brandon Troppens ECE 5736 - Professor Llamocca. 2. can be avoided. UMTS Since sign bits are not equal. This function takes in fraction and maximum bits the fraction needs to be expanded in binary. The result is put into the resultant sign bit. Indicate fractional values with a decimal point (.), and do not use commas. 7) Normalize the resultant mantissa (M3) if needed. 6) Compute the sum/difference of the mantissas depending on the sign bit S1 and S2. E = exponent vale obtained after normalization in step 2 + bias Bluetooth 3) Initial value of the exponent should be the larger of the 2 numbers, since we know exponent of X1 will be bigger , hence Initial exponent result E3 = E1. 3) E1 - E2 = (10000010 - 01111110) => (130-126)=4 9) Nan's are not supported. i.e. overflow has occurred ,the output should be set to infinity. So part of this code's result or operations are shown/done as bit wise computations. It automaticallly considers the N bit from the given Hex and computes the addition for the given exponent width. 0b0000000000000000000000000000000000000000000000000000000000000000. 8) If we had to perform subtraction, just change the sign bit of X2 to "1", amusing to try (computer output is red) (1+1e20)1e20= 0.000000 1+(1e201e20) = 1.000000 but everyone knows that (a+b)+c = a+(b+c) It can take Inf, MInf, NaN and can even take numbers like 0.001 or 1E-3. python FLP.py -s -ew 5 -fa 0x000D -fb 0x8083, This function converts the float given to its decimal value. M_A and M_B is between 1 - 1.9999999.and the range of the product is between (1 - 3.9999999)Therefore a 1 bit shift is required with the adjust of exponent. X3 in decimal = 10.3125. 1) Check if one/both operands = 0 or infinity. To make the equation 1, more clear let's consider the example in figure 1.lets try and represent the floating point binary word in the form of equation and convert it to equivalent decimal value. (1.m3 format) and the initial exponent result E3=E1 needs to be adjusted according to the normalization of mantissa. 0101_0000_0000_0000_0000_000 in actual it is (1.mantissa) 0101_0000_0000_0000_0000_000. The steps for adding floating-point numbers with the same sign are as follows: 1. I haven't tested with other browsers. exponents = all "0" or all "1". Equivalent floating point binary words are. Currently, it can convert the given decimal number to 32-bit float representaion and the corresponding float value stored. Enter a 32-bit value in hexadecimal and see it analyzed as a single-precision floating-point value. 5) Left shift the decimal point of mantissa (M2) by the exponent difference. It can also perfom basic four operations on upto 15 numbers. This normalizes the mantissa. Note : This program doesn't differentiate between qNan or sNan. 8. (This is the bias value for single precision IEEE floating point format). M1, M2 =>Mantissa bits of Number X1 & X2. Exponent: 10001000. 7) If (E1 + E2 - bias) >= to Emax then set the product to infinity. 1 bit = sign bit(s). In this example will convert the number 85.125 into IEEE 754 single precision. Press one of the four buttons to add, subtract, multiply, or Feature Summary : Computing addition/subtraction on N-bit floating point numbers with E-bit exponent; Conversion from decimal to floating point (N,E) and vice versa. divide the two numbers above the buttons and show the result below. Each form represents the exact value of the floating-point number. z-wave 8 = Biased exponent bits (e) 2) We assume that X1 has the larger absolute value of the 2 numbers. A brief overview of floating point multiplication algorithm have been explained below, 4. By default python3 FLP.py invokes FLP.py -h and displays information about all the switches it has with a small description about them. For example in the above fig 1: the mantissa represented is Floating-point addition is more complex than multiplication, brief overview of floating point addition algorithm have been explained below X3 = X1 + X2 X3 = (M1 x 2 E1) +/- (M2 x 2 E2) 1) X1 and X2 can only be added if the exponents are the same i.e E1=E2. Let us consider the IEEE 754 floating point format numbers X1 & X2 for our calculations. Normalize mantissa and adjust exponent if necessary. Binary (base 2) Octal (base 8) Decimal (base 10) Hexadecimal (base 16) Calculation examples: fractional binary: 1100.0101. hexadecimal: 8BA53. Biased Exponent (E1) =1000_0001 (2) = 129(10). M )2 E-bias They include values after (i) Alignment, (ii) Arithmetic, (iii . And apply it to floating point Adder, Division of IEEE 754 Floating point numbers (X1 & X2) is done by dividing the mantissas and subtracting the exponents. It also tries to minimise the use of advanced library functions. Floating-point addition is more complex than multiplication, brief overview of floating point addition algorithm have been explained below X3 = X1 + X2 X3 = (M1 x 2 E1) +/- (M2 x 2 E2) 1) X1 and X2 can only be added if the exponents are the same i.e E1=E2. Decimal result. It does not model any specific chip, but IEEE 754 Calculator This is a little calculator intended to help you understand the IEEE 754 standard for floating-point computation. field, instead of a bit pattern you can also enter a decimal If you enter a floating-point number in one of the three boxes This Floating point program has four main functionality and some additional features. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Add the mantissa's, 6) Normalization needed? The Resultant product of the 24 bits mantissas (M1 and M2) is = E1 + E2 -bias + (normalized exponent from step 2) floating point standard to Decimal point conversion,floating point Arithmetic,IEEE 754 standard Floating point multiplication Algorithm Binary floating point numbers are expressed in the form mantissa 2, start superscript, e, x, p, o, n, e, n, t, end superscript, 2 e x p o n e n t, e.g. IEEE 754 Converter (JavaScript), V0.22 Update There has been an update in the way the number is displayed. Similarly, the standard represents two different bit patterns for +INF and -INF. The simplified floating point multiplication chart is given in Figure 4. ES 1.00 highp criteria fulfilled Floating point numbers explorer Calculator shows internal representation of IEEE 754 floating point numbers, as it is stored in computer's memory. Antenna a bit ugly because the input boxes are a too wide.). Set the result to 0 or inf. 2) We assume that X1 has the larger absolute value of the 2 numbers. Truncate the result to 24 bits. This will filter inputs that would otherwise overflow to infinity or underflow to zero, but it will also prevent you from entering some hard halfway rounding cases. Essentially, you can enter what a computer program accepts as a floating-point literal, except without any suffix (like f). They include values after (i) Alignment, (ii) Arithmetic, (iii) Normalisation, (iv) Rounding steps. Exp_diff = (E1-E2). Let's consider two decimal numbers If E3 > Emax return overflow i.e. Mediump float calculator i.e. 2. Absolute value of of X1 should be greater than absolute value of X2, else swap the values such that Abs(X1) is greater than Abs(X2). 2) S1, the signed bit of the multiplicand is XOR'd with the multiplier signed bit of S2. This program performs floating point computation (add/sub) and format conversion operations. 2) Sign bit S3 = (S1 xor S1). ES 3.00 highp criteria fulfilled. using the syntax typically accepted in programming languages, 1) X1 and X2 can only be added if the exponents are the same i.e E1=E2. 2) Multiply the mantissa values including the "hidden one". You may need more than 17 digits to get the right 17 digits. You can enter numbers 4) The exponents of the Multiplier (E1) and the multiplicand (E2) bits are added and the base value is subtracted from the added result. It uses Gaurd,Round and sticky bit for making round to even tie to zero decision for rounding. 32-BIT FLOATING POINT CALCULATOR. 8) If any of the operands is infinity or if (E3>Emax) , Step 2: Convert the Integral Portion to Unsigned Binary. Floating-Point Calculator. python3 FLP.py -pp -ew 5 -n 16 -d2f 1E-7, Note: Hex and dec should be a string; sign=1 subtraction; displayIntermiate = True shows steps. 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