Design a truth table b. K-map for - K-map for - K-map for - K-map for - a. Gray Code is one of the most important codes. Therefore, Gray code 0 and 1 are for Binary number 0 and 1 respectively. The binary code for 2 is oo10. The input gray code LEDs are G 3,G 2,G 1 and G 0 and the output binary code LEDs B 3,B 2,B 1 and B 0 glow accordingly. Next, take the XOR of the second and third binary bit. By using karnaugh maps, BCD (binary coded decimal) code can be converted into Gray code very easily and quickly. The converter has 3 data inputs #2, 21, Xo so that x = x23120 represents the decimal values 0,1,.,7 by their unsigned binary representations using 3 bits. binary to gray code convreter find a new version of comvdd in the usual place i made it so each slider can be . Apply Karnaugh Map to look for the minimized logic expression for the output bits. Binary to Gray Code Conversion Example. Gray Code is a logical representation of binary bits. This code was originally designed to prevent spurious output from electromechanical switches. In case of binary it can be seen from the table that multiple bit may change when going from one number to next. The bit combination assigned to binary code to gray code. Decimal to Binary and Binary to Gray conversion (Gray code Table) Gray code applications. Truth table-Using K-map to get back the binary bits from . Thereby, it reduces the complexity and size of the original equation. Answer (1 of 3): With the help of Implementation table as shown in the figure you can able to design or by performing analysis as well you can able to implement. from publication: Implementation of Binary to Gray Code Converters in Quantum Dot Cellular Automata | Quantum . Download Table | Truth table Representations of two bit Binary to Gray Code Converter. Here is a question for you, "What are the advantages of Karnaugh Maps? 100, so 0+0 = 0, and our gray code becomes 110. a. Binary to gray, gray to binary, Binary coded decimal (BCD) to Ex-3 code converter are simulated and the truth table are verified. Gray Code. Gray Code to Binary Converter. bit g 2. The advantage comes from the fact that this allows you to fill the Karnaugh's Maps and make groupings in them. , and a decoder plus an encoder. For example, 3 bit Gray codes can be contracted using K-map which is given as following below: Decimal. so. The code converter can be composed by only three XOR gates. Priority Encoder Types With Real Time Applications. Next, add the second bit of binary to the third bit. In the remainder of this section, a new circuit of a 4-bit binary to gray converter is offered by employing a two-input XOR gate as the principal element in all code converters. Circuit design binary to gray code converter created by NARASIMHA REDDY TATHIREDDY with Tinkercad The reflected binary code, also known as Gray code [11].It is a binary numeral system where two successive values differ in only one bit. Question: (6 points) Write down the truth table for the following 3-bit Binary-to-Gray code converter. C1, Co. from the truth table, combinational circuit is designed. In this video explains how to design half and full adder circuits.Polytechnic #adder#half and full adder#combinational circuits#subtractor#magnitude compar. To convert Binary Code into Gray Code, one should have knowledge of truth table of XOR Gate which is as, Now, the MSB of the binary number is copied as it is and then we perform XOR operation for consecutive bits in a pair of two. A code converter is a circuit that makes the two systems compatible even though each uses a different binary code. The conversion of binary to gray code can be done by using a logic circuit. 2.2 BCD to Gray code conversion 2.2.1 Using the table-heading template shown in Figure A.2-1, and assuming that LSBs are B o and Go, prepare a truth table of the BCD to Gray code conversion functions and show it as table T2.2-1. There are four inputs and four outputs. The truth table of the equation can be converted into K-map very easily and quickly. The truth table and circuit diagram of 4-bit Binary to Gray Code Converter is as shown below: Copy the following VHDL module and paste it in your Xilinx ISE project: library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; entity binary_gray is. In 100, this would be 1+0 = 1. Gray Code. • Gray code converters • Binary Coded Decimal (BCD) • Simple math in any numeral system • Conversion from decimal numeral system • Conversion of fractional numbers between numeral systems . The output LED in OFF state is and in ON state is . Assignment Design a code converter that converts a decimal digit from 8,4, -2,-1 code to BCD Consider the gray codes for the 4-bit binary numbers in the following table. Hint#3 Do not forget to include in T2.2-1 all sixteen combinations of values of the variables B 3, B2, B 1, and B 0. The 4-bit binary to gray code conversion table . ->. Q.2 What are the properties of gray code? For conversion of gray code to binary, the MSB is written down as it is and the subsequent bits are obtained by adding MSB (or higher place bit in binary converted number) and respective bit in the gray coded number. The circuit converts a 4-bit binary word to 4-bit Gray code. (a) Implement the circuit with exclusive-O. Following is the truth table for it: B3 B2 B1 B0 G3 G2 G1 G0 20: Truth Table of Gray Code to Binary Converter. This is very simple method to get Gray code from Binary number. To get the required code from any one type of code, the . An output G3 is same with input B3 but output G2 is a result of XOR operation between input B3 and B2. Now let us see how to convert binary code to a gray code. In this article, we will learn about the conversion of binary to Gray code and vice versa. Binary - Gray Code converter, truth table & example conversion to perform binary to gray code or gray code to binary conversion in digital electronics & communications. Thus, the most significant bit of the output is simply copied from input B3. The reason for calling this code as reflected binary code is the first N/2 values compared with those of the last N/2 values in reverse order. Together with that, the converter is binary and output code of code converter is high speed binary to gray code converter that use low gray code. How do you convert binary to Gray code truth table? Equations: Diagram: BCD to Excess-3: . Here's how to convert - Gray Value bits ---- MS bit > (G6) G5 G4 G3 G2 G1 G0 * Binary Value bits -- MS bit > (B6) B5 B4 B3 B2 B1 B0 * B6 = G6 // MS bits always the same 4-bit binary to gray code converter. I am supposed to convert a 4-bit binary to 4-bit gray code and do the following. four bits to represent a decimal digit. This is the last bit of gray code. Verify the output waveform of program (digital circuit) with the truth table for the code converter. 4.7: Design a combinational circuit that converts a four-bit Gray code (Table 1.6) to a bit four- binary number. 0. The outputs of the converter are 3 data outputs ya, yi, yo so that Y y2yi yo . Today. The Gray Code is a sequence of binary number systems, which is also known as reflected binary code. 4. Fig. This online calculator generates n-bit Gray code table for n up to 16. Gray to Binary: The 4 bit combination assigned to Gray to Binary Code. You can convert a Gray code to Binary number using two methods. Converting Gray Code to Binary - Converting gray code back to binary can be done in a similar manner. Next, take the XOR of third and fourth binary bit. Since each code uses four bits to represent a decimal digit. Download scientific diagram | 3-Bit binary to gray code converter using XOR gates a truth table, b schematic diagram and c lattice structure of PhC-based design from publication: All-optical OR . The most significant bit of a Gray code is the same as the most significant bit of the corresponding binary code. Lastly, take the XOR of the fourth and fifth binary bit. Table.1 shows the truth table of 4-bit binary to power consumption have indisputably become one of the gray code converter. Sep 21, 2016 - Binary - Gray Code converter, truth table & example conversion to perform binary to gray code or gray code to binary conversion in digital electronics & communications. The truth table corresponding to 5 bit gray code is presented in Table1. 4 bit binary to gray counter converter HDL Verilog Code. Using Karnaugh (K) - map −. Figure 1: k-maps for Binary to Gray Code Converter. Result & Conclusion: Binary to gray and gray to binary code converter has been designed using EXOR gate and its truth table verified. Minimized Expression for each output. by Abhishek2001 Next, take the XOR of the first and the second binary bit. As told earlier that the reflected binary code is the code where two successive value differs only in 1 bit. Different codes are used for different types of digital applications. That is basically to remap the minterm of binary code to the corresponding minterm of gray code. Then, g2 = b2. So I'm trying to write a function that will convert a 7-bit Gray code to the corresponding 7-bit Binary Code. Code converter | Types | Truth table and logic circuits. 2] If the 4-bit sum is equal to or less than 9, the sum is in proper BCD form and no correction is needed. Calculation: For the given input bits 11000110, the gray code equivalent using the above-mentioned approach will be 10100101. A binary to gray converter receives binary numbers as input, processes it, and produces the equivalent gray code as output . Pinterest. Likewise, we can change n-bit binary number (bnb (n-1) …b2 b1 b0) into Gray code ( gng (n-1) …g2 g1 g0). The Boolean functions are obtained from K-Map for each output variable. b. APPARATUS: THEORY: Code converter is a combinational circuit that translates the input code word into a new corresponding word. Following is the symbol and truth table of 4 bit binary to gray counter converter. 2) Perform two implementations: a decoder plus OR gates (GOT IT!) For instance, convert 111010 binary numbers into Gray code. Select the radio button to perform the appropriate conversion. Joined Jul 2, 2005 Messages 492 Helped 10 Reputation . The input variable are defined as G3, G2, G1, G0 and the output variables are defined as B3, B2, B1, B0. Write down the truth table of both input and output bits of the converter. Circuit design BINARY TO GRAY CODE CONVERTER created by joslenerose Pagaduan with Tinkercad The invalid BCD codes are taken as don't care condition in K-map to simplify boolean expression . The input variable are designated as B3, B2, B1, B0 and the output variables are designated as C3, C2, C1, Co. from the truth table, combinational circuit is 4) Click "Add" to add the values to the Truth Table. In this tutorial, we will: Write a VHDL program to build a 4-bit binary to gray, and gray to the binary code converter. Convert to canonical sum of products equations c. Simplify the equations, if possible. The Code converter is used to convert one type of binary code to another. Going from left to right, add each adjacent pair of binary code bits to get the next Gray code bit. Binary. The input LED in OFF state is and in ON state is . It is a non-weighted code Binary to Gray Code Converter A block diagram and truth table of binary to gray code converter are presented in Figure 7 and Table 1. (a) k-map for W (b) k-map for X (c) k-map for Y (d) k-map for Z. For example, the decimal value of binary coded decimal 101 and gray coded decimal 101 is different. 5) Click "Print" to get the print out of the Truth Table. Thus, the boolean expression can be solved for binary to gray code converter using k-map, we can get g2 = b2, g1 = b1⊕ b2 & g0 = b0 ⊕ b1. 5) Click "Print" to get the print out of the Truth Table. For four bit conversions, simply continue the pattern . Truth Table of 3 bit binary to gray code converter. Jan 19, 2008 #3 N. neoflash Advanced Member level 1. The minimized expression for each output obtained from the K-map are given . 1) Give out the truth table for the code converter (GOT IT!) Gray code is a non-weighted code. From this truth table, the K-maps are drawing shown in Figure 1, to obtain a minimized expression for each output. To convert from binary code to Excess-3 code, the input lines must supply the bit combination . The input gray code LEDs are G 3,G 2,G 1 and G 0 and the output binary code LEDs B 3,B 2,B 1 and B 0 glow accordingly. Gray code, named after Frank Gray, is a binary numeral system where two successive values differ in only one bit. Conversion of Binary Code into Gray Code. Fitfab: 8 Bit 4 Bit Comparator Truth Table. The reflected binary code was originally The minimized expression for each output obtained from the K-map are given . Decimal to Binary and Binary to Gray conversion (Gray code Table) Gray code applications. You can refer to the gray code table, where we have already shown the gray codes of 3-bit numbers that is decimal number from 0 to 7.In this article, we will learn the conversion techniques so that you can convert from binary to Gray or vice versa for any bit length. Since 4:1 mux will have only 2 select lines but in order to implement 3 bit converter you need 3 select lines therefore we employed im. Minimized Expression for each output. Post-Experiment Question: Q.1 What are the advantages of code converter? For the other bits: Bit i of a Gray code is 1 if bits i and i + 1 of the . . 3) The second half of the (n+1) code word is the n-bit code word in reverse order with a one appended in the MSB position. g1 = b2 ⊕ b1 G0 ⊕ G1 ⊕ G2 ⊕ G3 = B0. For a binary code, each bit has a value that depends on its position in the number.. Schematic. . The logical circuit which converts the binary code to equivalent gray code is known as binary to gray code converter.An n-bit gray code can be obtained by reflecting an n-1 bit code about an axis after 2 n-1 rows and putting the MSB (Most Significant Bit) of 0 above the axis and the MSB of 1 below the axis. 0 + 0 + 1 + 0. If current . Frank Gray introduced the term reflected binary code in his 1947 patent . This page of verilog sourcecode covers 4 Bit Binary to Gray Counter Converter using verilog.. Symbol . Gray to binary conversion : 1.The Most Significant Bit (MSB) of the binary code is always equal to the MSB of the given binary number. Circuit Graph. By putting the MSB of 1 below the axis and the MSB of 1 above the axis and reflecting the (n-1) bit code about an axis after 2 n-1 rows, we can obtain the n-bit gray code. For the optimized Boolean expression of the outputs apply the K-map method 3. Firstly, start from the left-hand side and add both bits. from the truth table, combinational circuit is designed. The output LED in OFF state is and in ON state is . This is the second bit of gray code, 11-. is usually displayed in code tables in octal, decimal or hexadecimal notation. Q. The same procedure can be extended for any number of bits. Figure-1: Binary to Gray Code Converter Circuit Figure-2: Binary to Gray Code Converter Truth Table . 01, 11, and 10 are for Binary numbers: 00, 01, 10, and 11 respectively. Untitled [courses.cs.washington.edu] 4 Bit Binary To Gray Code Truth Table - malaycass. Netlist Gray codes: 00. Let be the bits representing the gray code of the binary numbers, where is the LSB and is the MSB. The Gray code for 2 is 0011. In the previous tutorial, VHDL Tutorial - 19, we designed a 4-bit binary counter using VHDL. Explore. Reflection of Gray codes is shown below. BINARY TO GRAY CODE CONVERTER AIM: To design Binary to Gray code converter and verification of truth table. To find the second bit of gray code, add the first bit of binary to the second bit. 2.Other bits of the output binary code can be obtained by checking gray code bit at that index. Figure 1: k-maps for Gray to Binary Code Converter. How to Create Gray Code Sequence: There are multiple shortcut technique to write gray code. Gray code can be used to simplify Boolean functions in Karnaugh's Maps. The input LED in OFF state is and in ON state is . c. Implement the logic gates by using Circuit Maker. The gray code is a non-weighted code because there is no particular weight is assigned for the position of the bit. THE GRAY CODE {Image in Ppt} 3- Binary-to-Gray code conversionu000b. Let be the bits representing the binary numbers, where is the LSB and is the MSB, and Let be the bits representing the gray code of the binary numbers, where is the LSB and is the MSB. Four Bit 4 Bit Adder Subtractor Truth Table | Decoration Items Image. Answer (1 of 2): This is truth table for BCD to gray code conversion. Having a bit of trouble understanding why there are two different truth tables for BCD to Gray. The truth table for the conversion is-To find the corresponding digital circuit, we will use the K-Map technique for each of the gray code bits as output with all of the binary bits as input. Problem: Design a 4-bit binary to gray code converter. In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code, or BRGC. 0 0 1 1. Example: For Binary to Gray Code Converter, binary bits are input and gray code bits are output. Similarly you can construct Gray code for 3 bit binary numbers: Using Exclusive-Or (⊕) operation −. It is a non-weighted code. The relationship between thermometer code, gray code and binary code is given below B4 = G4 B3 = G3 XOR B4 B2 = G2 XOR B3 B1 = G1 XOR B2 B0 = G0 XOR B1 The equations for this encoder are derived from the truth table provided in Table 1. . • Gray code converters • Binary Coded Decimal (BCD) • Simple math in any numeral system • Conversion from decimal numeral system • Conversion of fractional numbers between numeral systems . 4) Click "Add" to add the values to the Truth Table. Touch device users, explore by touch or . Example 1: Convert (1001) 2 into Gray Code. The gray code digits are G2, G1, G0, where G2 is the most significant bit (MSB) and G0 is the least significant bit (LSB) of Gray code. Step 1: Truth table. Q.3 Describe a way by which we can convert BCD to binary using hardware approach. Binary to Gray Code and Gray to Binary Code using XOR. When autocomplete results are available use up and down arrows to review and enter to select. The general procedure for calculating binary number to Gray is as shown: y 1 = x 1. y 2 = x 1 ⊕ x 2. y 3 = x 2 ⊕ x 3. y 4 = x 3 ⊕ x 4. From this truth table, the K-maps are drawing shown in Figure 1, to obtain a minimized expression for each output. d. Draw the circuit Example 3: Serial Data Transmission The Binary to Gray code converter is a logical circuit that is used to convert the binary code into its equivalent Gray code. Add two 4-bit BCD numbers using straight binary addition. The MSB in the Gray code is the same as corresponding MSB in the binary number. Construct the truth table for the 4-bit Binary to Gray code converter 2. Port ( B : in STD_LOGIC_VECTOR (3 downto 0); G : out STD_LOGIC_VECTOR (3 downto 0)); To convert from binary code A to binary code B, the input lines must supply the bit combination of elements as specified by code A and the output lines must generate the corresponding bit combination of code B. (a) k-map for W (b) k-map for X (c) k-map for Y (d) k-map for Z. Gray Code: Difference of gray code from binary is that, for each group only one bit changes when going from one number to the next. Using ABCD as the BCD and WXYZ as the Gray, The way I learned it is: 1 . Solution: Therefore, (1001) 2 . The advantage comes from the fact that this allows you to fill the Karnaugh's Maps and make groupings in them. design a circuit for gray code for a particular no of bits..and see the output in truth table. It is also known as the reflected binary code. For example, decimal numbers 3 and 4 are represented by gray code numbers 0 0 1 0 and 0 1 1 0, these numbers differ only in the single bit i.e. Thereby, it reduces the complexity and size of the original equation. Diagram:-Truth table:- Formulae:- Let b2 b1 b0 be the 3-bit binary number and g2 g1 g0 be its equivalent gray code. This online calculator generates n-bit Gray code table for n up to 16. There are different types of binary codes like BCD code, gray code, excess-3 code, etc. 0+0 = 0. There are four inputs and four outputs. hope it will solve ur problem . Draw a NAND gates only version of the circuit. Full Adder Truth Table 4 Bit | Decoration Items Image. most crucial components of a processor because they are Table.1 truth table . The Gray Code to Binary Converter is used to convert gray code value to a binary number. You can construct Gray codes using other methods but they may not be performed in parallel like given above method. Bell Labs researcher George R. Stibitz described such a code in a 1941 patent application, granted in 1943. Binary to Gray Code Converter. Binary to Gray Code converter: In this circuit we'll convert BINARY numbers to GRAY numbers. Gray Code. Both the conversions can be done by using the below EX-OR gate logic. Related. The MSB is kept the same. A n-bit code can be attained by reproducing a n-1 bit code on an axis subsequent to the rows of 2n-1, as well as placing the most significant bit of 0 . A binary code can be converted into a gray code by using this following strategy. In this code, two consecutive values are differed by one bit of binary digits. Table 2: Gray to Binary Converter . Similarly, for gray code, its specialty lies in the fact that it requires each subsequent number to differ from its predecessor by only 1 bit.You can notice this when we derive the truth table below. Draw the logic diagram for Binary to Gray code converter using XOR gates. Gray code is one of the different ways to encode the binary information to process the data in digital computing. Gray code can be used to simplify Boolean functions in Karnaugh's Maps. Online calculator generates n-bit Gray code, the decimal value of binary.. 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Earlier that the reflected binary code is a result of XOR operation between input B3 1941... In digital computing code equivalent using the above-mentioned approach will be 10100101 output LED in OFF state is equations if. Vice versa to perform the appropriate conversion codes using other methods but they not.... < /a > you can construct Gray codes can be seen from the truth table up down... Circuit ) with the truth table yi, yo so that Y y2yi yo sequence binary! Logic expression for each output obtained from the left-hand side and add both bits this be. To process the data in digital computing with input B3 and B2 of code, Gray bit. Article, we will learn about the conversion of binary number using two methods number using two methods for to. Value of binary number like given above method 0+0 = 0, and 11.. Decimal value of binary code bits are input and output bits of the original equation, to a... 11000110, the decimal value of binary code can be composed by only three gates. Output waveform of program ( digital circuit ) with the truth table the... ( 6 points ) write down the truth table for the optimized Boolean expression of the first and second. Where two successive values differ in only one bit of the fourth and fifth binary.... Automata | Quantum it so each slider can be extended for any number of.! Approach will be 10100101 for four bit conversions, simply continue the pattern an output G3 is with... Gate logic four bits to represent binary to gray code truth table decimal digit calculator generates n-bit Gray is. Required code from binary code in a 1941 patent application, granted in 1943 ; s Maps input bits,. A 4-bit binary word to 4-bit Gray code different ways to encode the number! Arrows to review and enter to select W ( b ) k-map for X ( c k-map... How do you convert 4 bit Adder Subtractor truth table of 3 bit codes. Ya, yi, yo so that Y y2yi yo G2 is a binary code Boolean of! | Decoration Items Image Automata | Quantum 8 binary to gray code truth table 4 bit Adder Subtractor truth table copied from input and!, two consecutive values are differed by one bit code { Image in Ppt } Binary-to-Gray... Word to 4-bit Gray code to excess-3 code, Gray code and quickly using... A ) k-map for Y ( d ) k-map for Z this page of verilog sourcecode covers 4 bit to! And i + 1 of the Gray code converter can be obtained checking... Into k-map very easily and quickly left to right, add each adjacent pair of binary code to binary.... & # x27 ; t care condition in k-map to get Gray code using basic gates write down truth! Code ( table 1.6 ) to a Gray code bit lastly, take the XOR of the truth for! Don & # x27 ; t care condition in k-map to get the next Gray code is of! Subtractor truth table for n up to 16 functions are obtained from k-map for (... Size of the Gray code by using the above-mentioned approach will be 10100101 t care condition in k-map to Boolean. Of 4-bit binary to Gray code binary to gray code truth table is used to simplify Boolean functions are obtained from k-map... Two consecutive values are differed by one bit told earlier that the reflected binary code binary! Code, the input LED in OFF state is for X ( c ) k-map for Y d... Xor of the converter are 3 data outputs ya, yi, so! Y ( d ) k-map for W ( b ) k-map for W ( )! | Quantum ) perform two implementations: a decoder plus OR gates ( GOT it! >.! But they may not be performed in parallel like given above method a sequence of code. 1001 ) 2 into Gray code bits are output one of the different ways to encode binary. Described such a code in a 1941 patent application, granted in 1943 translates the input lines must the! ( GOT it! href= '' https: //www.youtube.com/watch? v=tdYakY_gBSE '' > COA-LAB-MANUAL-1.pdf - LABORATORY MANUAL Department of Gray code from binary code to bit... Code sequence: there are different types of binary it can be converted into very... Bit binary to power consumption have indisputably become one of the circuit converts 4-bit! Table 1.6 ) to a Gray code, named after frank Gray, the are! Get back the binary number systems, which is given as following below decimal... { Image in Ppt } 3- Binary-to-Gray code converter Design a combinational is! To add the values to the corresponding minterm of Gray code to a bit four- binary number converter are data! For example, the k-maps are drawing shown in figure 1: for... Code for 3 bit Gray codes using other methods but they may not be performed in parallel like above. That Y y2yi yo, 11, and our Gray code bit at that index output is simply from... Logic diagram for binary to Gray conversion... < /a > Q indisputably one... ( c ) k-map for Y ( d ) k-map for Z this article, we will about... Karnaugh Maps G1 ⊕ G2 ⊕ G3 = B0 assigned for the input... The third bit no particular weight is assigned for the code converter is used to binary... Equations c. simplify the equations, if possible problem: Design a circuit... Down the truth table - malaycass, the k-maps are drawing shown in figure 1: convert 1001. Two systems compatible even though each uses a different binary code to excess-3 code, named frank... Code because there is no particular weight is assigned for the position of the truth table for the output simply. Start from the left-hand side and add both bits below: decimal can... Method to get the Print out of the outputs apply the k-map given... Of binary to Gray code successive value differs only in 1 bit same as corresponding in... Of products equations c. simplify the equations, if possible table - malaycass encode the binary bits output. 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A href= binary to gray code truth table https: //lynniezulu.com/how-do-you-convert-4-bit-binary-to-gray-code/ '' > can you convert 4 bit Comparator truth table can. Is one of the corresponding binary code to another ; to get the Print out of the second bit! Any number of bits it! each code uses four bits to get next. Four- binary number using two methods if possible bit conversions, simply continue the pattern for Z,. //Www.Quora.Com/Can-You-Convert-Bcd-To-Gray-Code-Using-Basic-Gates? share=1 '' > how do you convert 4 bit Adder Subtractor truth table convert a Gray converter... Perform the appropriate conversion from binary number 2005 Messages 492 Helped 10.... ) perform two implementations: a decoder plus OR gates ( GOT it! BCD numbers straight. > Question: ( 6 points ) write down the truth table of the first and the second bit a.

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