What is the difference between binary arithmetic and Boolean arithmetic?

Answer 1

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

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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.