Octal numbers therefore have a range of just “8” digits, (0, 1, 2, 3, 4, 5, 6, 7) making them a Base-8 numbering system and therefore, q is equal to “8”….Octal Numbers.

Decimal Number	3-bit Binary Number	Octal Number
5	101	5
6	110	6
7	111	7
8	001 000	10 (1+0)

The octal number system (or shortly oct) uses the number 8 as its base (radix). As a base-8 numeral system, it uses eight symbols: The numbers from 0 to 7, namely 0, 1, 2, 3, 4, 5, 6 and 7….Decimal to Octal Conversion Chart Table.

Decimal	Octal
8	10
9	11
10	12
11	13

Decimal to Octal Table

Decimal	Equivalent Octal Number
10	12
11	13
12	14
13	15

Decimal 122 to Octal Conversion

Decimal	Octal	Binary
122	172	1111010
122.5	172.4	1111010.1
123	173	1111011
123.5	173.4	1111011.1

The base-2 value of 11012 is equal to base-10 value of 1310….Binary 1101 to Decimal Conversion.

Binary	Decimal	Hex
1101	13	D
1101.1	13.5	D.8
1110	14	E

We use only 3 bits to represent Octal Numbers. Each group will have a distinct value between 000 and 111. Note: Octal number system supports only digits from 0 to 7. Beyond 7, such as 8 and 9 are not octal digits.

BCD-to-Decimal Conversion Simply divide the binary number into groups of four digits, starting with the least significant digit and then write the decimal digit represented by each 4-bit group.

BCD is very common in electronic systems where a numeric value is to be displayed, especially in systems consisting solely of digital logic, and not containing a microprocessor.

BCD Codes. The BCD8421 code is so called because each of the four bits is given a ‘weighting’ according to its column value in the binary system. The least significant bit (lsb) has the weight or value 1, the next bit, going left, the value 2. 2410 in 8 bit binary would be 00011000 but in BCD8421 is 0010 0100.

A Digital Decoder IC, is a device which converts one digital format into another and one of the most commonly used devices for doing this is called the Binary Coded Decimal (BCD) to 7-Segment Display Decoder.

The Aiken code (also known as 2421 code) is a complementary binary-coded decimal (BCD) code. A group of four bits is assigned to the decimal digits from 0 to 9 according to the following table.

Data Structure and AlgorithmsMathematicsDigital Electronics. The excess-3 code (or XS3) is a non-weighted code used to express code used to express decimal numbers. It is a self-complementary binary coded decimal (BCD) code and numerical system which has biased representation.

This code has all positive weights. Sum of weights of unnatural BCD codes is equal to 9. It is a self-complementing code. Self-complementing codes provide the 9’s complement of a decimal number, just by interchanging 1’s and 0’s in its equivalent 2421 representation.

In this tutorial, we will learn about one of the basic requirements of digital electronics i.e., the Binary Codes of the Binary Number System. Some of the popular Binary Codes are BCD (8421), 2421, 5211, Excess-3, Gray….Gray Code.

Decimal Number	Binary Code	Gray Code
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111

Gray Code system is a binary number system in which every successive pair of numbers differs in only one bit. For example, the states of a system may change from 3(011) to 4(100) as- 011 — 001 — 101 — 100.

In Gray code, each successive number only requires one bit to change value….Those Who Remember Gray Code.

Decimal	Gray
0	000
1	001	One bit changes value
2	011	One bit changes value
3	010	One bit changes value

Advantage of grey code over binary is only one bit changes for each step. This will be useful in circuits that are sensitive to glitches. Example: When you use grey code to trim output impedance of IO blocks, there wont be a huge jump in codes momentarily that would cause reflection.

From Google search: Gray Code is Reflective Binary code. One of the main disadvantages of the Gray code is that it is very difficult to come up with an arithmetic logic unit to support Gray code.

The advantage is that when numbers are changing frequently, the logic gates are turning ON and OFF frequently and so are the transistors switching which characterizes power consumption of the circuit; since only one bit is changing from number to number, switching is reduced and hence is the power consumption.

Originally Answered: Why is the gray code used in K-map? In k-map the same simplification of Boolean expression is done by pairing adjacent 1’s for reducing variables. so if gray code is used in K-map the adjacent cells can be easily paired as they differ by only one bit and final expression can be obtained.

These codes are used to look at clarity as well as error modification in binary communications. The conversion of binary to gray code can be done by using a logic circuit. The gray code is a non-weighted code because there is no particular weight is assigned for the position of the bit.

Gray code is a form of binary and the most popular absolute encoder output type. Gray Code is a form of binary that uses a different method of incrementing from one number to the next. With Gray Code, only one bit changes state from one position to another.

A Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1. The term Gray code is often used to refer to a “reflected” code, or more specifically still, the binary reflected Gray code.