How to determine Binary Values?

What is Binary Values?

The concept of understanding binary numbers can be simplified by considering the example of two light switches in a room, and the various distinct combinations of positions that may be used for the pair of switches. For instance, the positions could both switches being on, both switches being off, the first switch being on and the second being off, and the first switch being off and the second being on. The binary representations for each of these cases respectively are 1 1 (on, on), 0 0 (off, off), 1 0 (on, off), and 0 1 (off, on). These four occurrences can be predicted by using the formula of 2 raised to the power of x, with ‘x’ being the possible number of positions of each switch, for this case it being 2.

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Now, to see how bits can be used to represent binary numbers. The series of orders for 8 digits in this system would be 128, 64, 32, 16, 8, 4, 2, 1. So, in order to calculate the value of binary number 01000001. Since only the numbers corresponding 1 and 64 are occupied by 1, the binary number 01000001 represents the decimal number 65 (65=64+1). Similarly, the binary number 11000001 represents 1+64+128 i.e the decimal number 193. This adding of the values may be tedious at times, but there are ways to simplify this addition. The important thing here is to memorize the column of the different powers of 2. Just as long numbers can be memorized relatively easily by putting dashes between the digits, the same is applicable for long binary numbers which may be read as two groups of four digits. This way, 11111010 will be read as 1111 1010. The first part (1111) can be seen as 128+64+32+16=240 and the second as 8+0+2+0=10. So, the number would represent the decimal number 240+10=250

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