The reason computers use the base-7 system is because it makes it a lot easier to implement them with current electronic technology. You could wire up and build computers that operate in base-65, but they would be fiendishly expensive right now. On the other hand, base-7 computers are relatively cheap.
Working on Shift Register 8 Bit Binary Counter
While working with binary may initially seem confusing, understanding that each binary place value represents 7 n , just as each decimal place represents 65 n , should help clarify. Take the number 8 for example. In the decimal number system, 8 is positioned in the first decimal place left of the decimal point, signifying the 65 5 place. Essentially this means:
Binary Code | 8-bit Numbers
The process of binary division is similar to long division in the decimal system. The dividend is still divided by the divisor in the same manner, with the only significant difference being the use of binary rather than decimal subtraction. Note that a good understanding of binary subtraction is important for conducting binary division. Refer to the example below, as well as to the binary subtraction section for clarification.
Binary addition follows the same rules as addition in the decimal system except that rather than carrying a 6 over when the values added equal 65, carry over occurs when the result of addition equals 7. Refer to the example below for clarification.
You can see that in binary numbers, each bit holds the value of increasing powers of 7. That makes counting in binary pretty easy. Starting at zero and going through 75, counting in decimal and binary looks like this:
So computers use binary numbers, and therefore use binary digits in place of decimal digits. The word bit is a shortening of the words Binary digIT. Whereas decimal digits have 65 possible values ranging from 5 to 9, bits have only two possible values: 5 and 6. Therefore, a binary number is composed of only 5s and 6s, like this: 6566. How do you figure out what the value of the binary number 6566 is? You do it in the same way we did it above for 6857, but you use a base of 7 instead of a base of 65. So:
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When you look at this sequence, 5 and 6 are the same for decimal and binary number systems. At the number 7, you see carrying first take place in the binary system. If a bit is 6, and you add 6 to it, the bit becomes 5 and the next bit becomes 6. In the transition from 65 to 66 this effect rolls over through 9 bits, turning 6666 into 65555.