This article is part II of my refutation of Mr. Missionary. The article will focus on what Mr. Missionary said:

“So obsessively naïve in trying to prove me wrong that he came with 2+2= as an example of an absolute “certainty” without respecting the reality that the decimal base applied is Mathematically changeable for instance binary base numbers where 2+2 = 100. Yet the base of a numerical system which varies from language to language or civilization to civilization determines the values of its digital sequence, characters, and values.”

Without much ado, 2 + 2 = 4 is decimal base and it is a certainty. ** Here is where your lack of depth once again shows. One of the principles of the philosophy of numbers is that, if you add two even numbers, the result will be an even number**. When two odd numbers are added what result is reached? These underlying principles have absolutely nothing to with what language is used, or civilization and the like. Let go further and define the “even” so that Mr. Missionary is not confused. The “Even” is that which can be divided into two equal parts without a unit intervening in the middle. You can infer from this definition what the definition of odd is. Of course, I am talking about even and odd numbers.

How on earth can a person use decimal base numbers and arrived at a result that is a binary base number without first converting all the numbers involved to binary base first? The number 2 in binary base numerical is represented as 1,0. The question is how does one gets to the 1s and 0s?

First, I ask Mr. Missionary, what civilization speaks in digital sequence or __communicate solely__ in binary base numbers, or better, uses base – 10 number when doing addition and end up with binary base numbers for the results? You are incredible! Research what binary base numbers are, and see if there was a time when the method of counting or calculating were primarily based on binary base.

Mr. Missionary talks about binary base numbers without explaining what it is. Bi is a prefix that means two. Binary base number means a number that has a base two. How to write 12_{10 } (Twelve base- 10) as binary number? First you have to convert to base-two column, the analogue of base- 10 columns. In base- 10, you have columns or places for 10^{0 }= 1, 10^{1 }= 10, 10^{2} = 100, 10^{3 }= 1000 and so forth. It is obvious that 10^{2 }= 10 x10 =100.

Let me now turn to base two, which means binary base. Here too you have columns or places just like decimal base numbers for 2^{0 }= 1, 2^{1 }= 2, __2 ^{2} = 4__, 2

^{3 }= 8, 2

^{4}= 16 and so forth. Now Mr. Missionary said that in binary base number, 2 + 2 = 100. Seriously! 2 in binary base number is a 1 and a 0. If a 1 and a 0 is added to another 1 and a 0, how does it become 100? It does not by addition, but if one calls the 1 and the 0 ten (10), which by the way shift to decimal base number then 10 x 10 = 100, and not 10 + 10, which is 20. So where does Mr. Missionary get his 2 + 2 = 100. Let me explain:

The first column in base-two math is the unit column. When you get to “two”, you find that there is __no single solitary digit that stand for “two”__ in base-two math. Instead, you put a “1” in the twos column and a “0” in the units column, indicating “1 two and zero one”: To compare base-ten and base two, the base-ten “two (2_{10}) is written in binary as 10_{2. }

_{ }

For example, a “three” in base two is actually “ 1 two and 1 one, and it is written as 11_{2. } What does (1 two) and (1 one) = 3 means? This simply means in 3 there is one 2 and the remainder being 1. 2 +1 = 3. Of course, I am explaining this in ten base numerical language.

How about “Four”? Here is how it looks: ** You zero out the twos column and the units columns (means you write zeros in them) and put a “1” in the fours column, 4_{10 }is written in binary form as 100_{2.}** The following will make this clear:

Decimal (base 10) Binary (base 2)

0 means 0 ones

- 1 one and zero one
- 10, (1 two and zero one)
- 11, (1 two and 1 one)
- 100, (1 four, 0 twos and 0 ones)
- 101, (1 four, 0 twos and 1 one)
- 110, (1 four, 1 two and 0 one)
- 111, (1 four, 1 twos and 1 one)
- 1000, (1 eight 0 four, 0 twos and 0 ones)
- 1010, (1 eight, 0 four, 0 twos, and 1 one)
- 1010, (1 eight, 0 fours, 1 twos and 0 one)
- 1011, (1 eight, 0 four, 1 twos and 1 ones)
- 1100, (1 eight, 1 four, 0 twos, and 0 ones)
- 1101, (1 eight, 1 four, 0 twos, and 1 ones)
- 1110, (1 eight, 1 four, 1 twos and 1 one)
- 1111, (1 eight, 1 four, 1 twos and 1 one)
- 10,000, (1 sixteen, 0 eights, 0 fours, 0 twos, and o ones)

I said 2 + 2 = 4 is a certainty. Mr. Missionary said in binary base 2 + 2 = 100. But binary base does not use 2. Instead, 2 in binary-base is 1,0 (1 two and zero ones) because of the columns or places. To make a direct correlation from 2 + 2 to binary base would be 10 + 10. 2_{10 }(ten-base “two”) is written in binary as 10^{2.}, Instead of saying 2 + 2, one would then have to say 10 + 10 or 1,0 + 1, 0^{ . }Binary base goes with ones and zero and not 2s and the like. Now 10 + 10 or if you want to separate the 1 from the zero by using a comma like 1,0 + 1,0, is not going to yield 100 unless the plus sing is changed to a multiplication sign, but my assertion was 2 + 2 = 4. Even if the change of the plus sign to a multiplication sign is assumed, a person will never say two when calculating in binary base but the number that represent two being 1,0.

For example, Convert 101100101_{2} to base-ten number and list the digits in order, and count them of from the right starting with zero:

- Digits from binary number:
**101100101** - Power 2 (base) corresponding to each digit: 876543210

To convert each digit to the power of two that it represents:

(**1**x2^{8}) +(**0** x2^{7})+(**1**x2^{6})+(**1**x2^{5})+(**0**x2^{4})+(**0**x2^{3})+(**1**x2^{2})+(**0**x2^{1})+(**1**x2^{0}) =

(1×256)+(0x128)+(1×64)+(1×32)+(0x16)+(0x8)+(1×4)+(0x2)+(1×1) =

256+64+32+4+1=357 then 101100101 converts to 357_{10}

_{ }

Converting decimal to binary just divide by 2. Convert 357_{10} to binary base:

2÷ 2= 1, remainder 0

2 ÷ 5 =2, remainder 1

2 ÷11=5, remainder 1

2 ÷ 22=11, remainder 0

2 ÷ 44=22, remainder 0

2 ÷ 89=44, remainder 1

2 ÷ 178=89, remainder 0

2÷357= 178, remainder 1

List the remainders from top to bottom: 101100101. Here one can see that the first unit to count is the result of ÷ 2 = 1, then the remainder 0 and then every subsequent remainder. As is clear, 357_{10 }in binary-base is 101100101_{2}.

**Summary**: Binary numerical system is based on two characters, “0” and “1” to represent all possible numbers. In other words, it is a base 2 system. Numbers are represented as follows: 0 = 0, 1 = 1, and from 2 the principle of addition is used. Addition in base – 2 is similar to addition in base – 10. To increment a number by one:

- If the number ends in a zero, the zero is replaced by one: e.g., the binary 100 is represented as (4). Now 5 would then be 100 (4) + (1) = 101 (5). Here the base – 10 numbers are used in brackets for comparison.

- If the number ends with a one but is not all ones, the first zero from the right is replaced by one while all the ones following it on the right becomes zero: 1011 (11) + 1 = 1100.

- If the original number is all ones, then they are changed to zeros, and a one is added at the front: 111 (7) + 1 (1) = 1000 (8). If you disregard the base – 10 numbers in the brackets, this is what you get: 111 + 1 = 1000. How on earth does 111 + 1 = 1000? To translate, what number can you add a 1 and the total is 8? As anyone can see, 111, which is binary base, is 7 in base – 10 and of course 1 is 1 in either system.

So, it is preposterous to say that 2 + 2 = 100, because that is adding base – 10 numbers and giving your result in binary base without first converting 2 + 2 to binary base. If one converts 2 + 2 from base – 10 to binary base, one has to also convert the plus sign to multiplication sign, which would look like this 10 x 10 = 100. You see your confusion Mr. Missionary? I posited a base –10: 2 + 2 = 4, you countered and said in binary base 2 + 2 = 100 without first converting 2 + 2 to binary base. And you thought you refuted the certainty of 2 + 2 = 4. It is always advisable to speak about things that you have a clue.

- To add two numbers, they are aligned under each other, and for each place, 0 + 0 produces 0, 1 + 0 produces 1, 1 +1 produces 10, where 0 is put in that position and the 1 is carried over to the next position. For example, in this case, working from right to left:

- 1 + 1 produce 0, with one carried over;
- 1 +1+1 produces 1 with one carried over;
- 1 + 1 produces 0 with one carried over;
- 1 +1+1 produces 1 with one carried over;
- 1+1 produces 10, so putting this together, you get 101010.

Subtraction works using the same principle except instead of carrying over ones, we “borrow” one. Multiplication is also similar to base-10 multiplication. Multiplying by 0 results in a 0, while multiplying by 1 is 1. So for example 101(5) x 10(2) = 1010(10), i.e., 5 x 2 =10 base -10, and 101 x 10 = 1010.

If one goes by Mr. Missionary’s assertion, then 5 + 2 = 1010, that is without first converting 5 + 2 to binary base. Let the readers judge! As is clear, Mr. Missionary, 2 + 2 = 4 is a certainty. You confused the two bases not knowing what you were talking about. If you have known what you were talking about, then you would not have made the absurd assertion that 2 + 2 = 100 without first converting the base-10 into binary base. In other words, 2 + 2 = 100 does not exist. You either say 2 + 2 = the base -10 result 4 or you convert 2 + 2 into binary base and come up with the result in binary base numerical. Because you are into scoring points, you thought you got something when you did not. Had you had depth, you would have seen the error in your assertion. And I need not get in what Gottfried Leibniz, the father of modern binary had to say about the matter in his article “Explication de l’Arithmetique Binaire” or “Explanation of the binary arithmetic.”

**The certainty of God’s existence is up next! “The fear of the Lord is the beginning of knowledge; fools despise wisdom and instruction.” Proverbs 1:7**

Ends

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