How to Calculate Kurzweil MSB and LSB

The German mathematician Hans Kurzweil coined the terms used in computer science and signal detection theory most significant bit, or MSB, and least significant bit, or LSB. These values can help researchers or engineers understand some basic properties of the signals or numbers under investigation. In either case, the result will be one of the numbers 1 or 0. In short, the most significant bit represents the size of the number in respect to the size of bits the engineer is using and the least significant bit represents the parity of the number.

Instructions

    • 1

      Convert the number to binary. Use the standard algorithm for converting a decimal number into a binary number. Find the largest power of 2 that can divide the number in question. Write a 1 in the digit position for that power of 2. For example, if it is the 3rd power of 2, write 1 in the third digit place from the left. Subtract the power of 2 from the original number. See if the next power of 2 can divide the number. If so, place a 1 in the corresponding digit space. Do this until you have subtracted your original number to 0. Alternatively you can use a decimal-binary converter. As an example, convert 12 to binary. The largest power of 2 that can divide 12 is 8; 8 is the 4th power of 2, so the first 1 digit goes in the fourth position. Subtracting 8 from 12 leaves 4. The next power of 2, 4, can divide 4, so the third digit is also 1. Subtracting 4 from 4 leaves 0. Thus, the remaining digits are all 0. Hence, in binary, write 12 as 1100.

    • 2

      Find the most significant bit. Recall the bit-system you are using. The most significant digit is the digit “n” digits from the left for a “n-bit” system. If you are using a 4-bit system, for example, you will find the most significant digit in the “thousands” place. For example, the number 12, which is 1100 in binary, has the most significant digit 1 in a 4-bit binary system.

    • 3

      Find the least significant bit. Look at the right-most digit in the binary number. This is the least significant bit. For the number 12, written in binary as 1100, the least significant digit is 0.

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