201
100101
100101
It is 100101
Decimal 37 expressed in binary form is 100101 (or 00100101).
MX 175 F 1979 = Start Engine#: 3M2-000101 MX 175 G 1980 = Start Engine#: 3M2-100101
This gentleman claims there were 10,300 made: http://www.1971xs1b.com/ His claim seems to be supported by serial numbers which start at 007101 for the XS1b and 100101 for the XS2 (http://www.biker.net/650parts_index.html)
A shift register is used for multiplying and devision. If a binary number of say Bin. 100101 (37 Dec.) is multiplied by 2 the bits have to be left shifted one time and the number will then be Bin. 1001010 (74 Dec.) and to divide by 2 the bits have to be right shifted
100101 1 times 2^0 = 1 PLUS 0 times 2^1 = 0 PLUS 1 times 2^2 = 4 PLUS 0 times 2^3 = 0 PLUS 0 times 2^4 = 0 PLUS 1 times 2^5 = 32 EQUALS 37
Look at this sequence:103 = 1000102 = 100101 = 10100 = 1On the left side, the exponent reduces by one at a time; on the right side, the number decreases by a factor 10. So, the last step, 10 to the power zero = 1, is quite logical.Note that this doesn't PROVE anything; in fact, the definition "x to the power zero = 1" might be considered an arbitrary definition. The sequence above only shows that the definition makes sense.
That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.
Boolean arithmetic has only two values: 0 and 1 or FALSE and TRUE. The result of a Boolean operation is also one of these values. Although binary arithmetic is also based on only two values, 0 and 1, these digits can be combined, using the place value structure, to generate all numerical values. Thus Boolean: TRUE + TRUE = TRUE Binary: 1 + 1 = 10 ------------------------------------------------------------------------------------------------ Binary arithmetic is like basic arithmetic but with the base 2. When we read 1,2,3,4,5...9, we are reading in the base 10. For example, if we want to write the number 23 in base 10, we would get this: 2(10^1)+3(10^0) = 23. if we want to interpret the number 23 in binary or base 2, we would have 10111. Think about the expansion form of the number but in base 2. 1(2^4)+0(2^3)+1(2^2)+1(2^1)+1(2^0) = 23 = 2(10^1)+3(10^0). Try to set your mind in the base 2 format. The addition and subtraction of binary will sink in too.The previous example(not written by me) is great example of the basics. Another example of binary add./sub. would be 100101+101. The 1+1 does equal 10, but in my example, the 1 is carried and the 0 in left. Similar to 96+5. We don't leave 9 6 + 5 ----- 9(11) we leave 101. Same with 100101+101 1 1 100101 + 101 (1+1 = 10; leave the zero and carry the one) -------- 101010 Just let the logic sink in and you will realize that format is not bad For subtraction, same logic but instead of carry there's borrow for example 1 11 100 -11 (borrow the 1 ) ----- 001 It's sort of weird but it like: 8(13) 9 3 (borrow a 1 from the 9 to make 13) + 5 ----- 9(11) from the 1+1 =10, we can change it to: 10-1=1; Boolean Arithmetic (a.k.a logic math) is used in Computer Science to determine true of false using T or F, or 1(true) or 0(false). We use this math to set values on conditions and figure out a result. This is total different from binary math. Binary Math is the math of computers, Boolean Math is using inductive reasoning math. Totally different applications.
(Note that 0 to the power 0 is not defined. Any other number to the power 0 are always equal to 1.)If it is defined that way, the following rule is still valid with powers of zero: xa times xb = xa+b. If you use a zero exponent, you have xa times x0 = xa. Now, which number can you replace for x0 in this equation? - 1, of course.Another way of looking at it is to consider the following sequence:103 = 1000102 = 100101 = 10100 = ???In the left column, the exponent reduces by one every time, in the right column, the result gets reduced by a factor of 10. So, what number should you replace for the question marks? - If you continue the sequence, you get 10/10 = 1. By the same token, just by continuing the sequence, it should be obvious that 10 to the power -1 would be 1/10.