Prove that every binary number n that ends in 0 is evenSolut

Prove that every binary number n that ends in 0 is even.

Let the binary number end in 1

Let the said binary number be abcd1

We will prove this by contradiction....

abcd1 = a * 10^4 + b * 10^3 + c*10^2 + d*10^1 + 1*10^0
abcd1 = 10000a + 1000b + 100c + 10d + 1

Now, in this number, 10000a , 1000b, 100c and 10d are also divisible by 2 because the numbers
10000 , 1000 , 100 and 10 are divisible by 2

So, terms 10000a , 1000b , 100c and 10d are even

So, abcd1 = even + even + even + even + odd

even+even+even+even is still an even number

So, abcd1 = even + odd

even + odd number is ALWAYS odd (as examples : 2 + 3 = 5 , 5 + 6 = 11)

abcd1 = odd

Hence proved by contradiction that for the binary number to be even, the last numeral must be a ZERO