So for example, converting a Binary to Decimal number would be: Decimal Digit Valueīy adding together ALL the decimal number values from right to left at the positions that are represented by a “ 1” gives us: (256) + (64) + (32) + (4) + (1) = 357 10 or three hundred and fifty seven as a decimal number. Then the first digit has a weight of 1 ( 2 0 ), the second digit has a weight of 2 ( 2 1 ), the third a weight of 4 ( 2 2 ), the fourth a weight of 8 ( 2 3 ) and so on. In the binary number system, the weight of each digit increases by a factor of 2 as shown.

We saw above that in the decimal number system, the weight of each digit from right to left increases by a factor of 10. But as it is a binary digit it can only have a value of either “1” or “0” therefore, q is equal to “2” (0 or 1) with its position indicating its weight within the string.Īs the decimal number is a weighted number, converting from decimal to binary (base 10 to base 2) will also produce a weighted binary number with the right-hand most bit being the Least Significant Bit or LSB, and the left-hand most bit being the Most Significant Bit or MSB, and we can represent this as: Representation of a Binary Number MSB In the binary numbering system, a binary number such as 101100101 is expressed with a string of “1’s” and “0’s” with each digit along the string from right to left having a value twice that of the previous digit. But unlike the decimal system which uses powers of ten, the binary numbering system works on powers of two giving a binary to decimal conversion from base-2 to base-10.ĭigital logic and computer systems use just two values or states to represent a condition, a logic level “1” or a logic level “0”, and each “0” and “1” is considered to be a single digit in a Base-of-2 (bi) or “binary numbering system”.

The Binary Numbering System is the most fundamental numbering system in all digital and computer based systems and binary numbers follow the same set of rules as the decimal numbering system. In other words, the digit 6 is the MSD since its left most position carries the most weight, and the number 3 is the LSD as its right most position carries the least weight.

Where in this decimal numbering system example, the left most digit is the most significant digit, or MSD, and the right most digit is the least significant digit or LSD. Or it can be written in polynomial form as: Or it can be written reflecting the weight of each digit as: For example: N = 6163 10 (Six Thousand One Hundred and Sixty Three) in a decimal format is equal to: The value of any decimal number will be equal to the sum of its digits multiplied by their respective weights. For example, 20 (twenty) is the same as saying 2 x 10 1 and therefore 400 (four hundred) is the same as saying 4 x 10 2. So we can see that the “decimal numbering system” has a base of 10 or modulo-10 (sometimes called MOD-10) with the position of each digit in the decimal system indicating the magnitude or weight of that digit as q is equal to “10” (0 through 9). Likewise, for fractional numbers the weight of the number becomes more negative as we move from left to right, 10 -1, 10 -2, 10 -3 etc. Then each position to the left of the decimal point indicates an increased positive power of 10.

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