The sum of 111011base2,11111base2 and 10000 is 10m10n0base2.Find the value of m and n?
Well, well, well. It seems like we have some binary arithmetic going on here. Let's break it down and solve it step by step.
First, let's convert the given numbers to decimal form:
111011(base2) = 59
11111(base2) = 31
10000(base2) = 16
So, we have the equation:
59 + 31 + 16 = 10m10n0(base2)
Combining like terms, we get:
106 = 10m10n0(base2)
Now, let's express 106 in binary form:
106(base10) = 1101010(base2)
Comparing this to 10m10n0(base2), we can deduce that:
m = 1
n = 0
Therefore, the value of m is 1 and the value of n is 0. Voila! We cracked it!
To find the value of m and n, we'll need to convert the given numbers from binary to decimal.
111011base2 in decimal is 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 59.
11111base2 in decimal is 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 31.
10000base2 in decimal is 1 * 2^4 = 16.
Now, let's look at the given sum, 10m10n0base2, in decimal.
10m10n0base2 in decimal is 1 * 2^6 + 0 * 2^5 + m * 2^4 + 1 * 2^3 + 0 * 2^2 + n * 2^1 + 0 * 2^0.
From the given information above, we can form the equation:
1 * 2^6 + 0 * 2^5 + m * 2^4 + 1 * 2^3 + 0 * 2^2 + n * 2^1 + 0 * 2^0 = 59 + 31 + 16.
Simplifying the equation, we have:
64 + 16m + 8 + 2n = 106.
Rearranging the equation, we get:
16m + 2n = 34.
Now, we need to determine the values of m and n that satisfy this equation.
Let's try different values for m and n:
For m = 1 and n = 9, we have 16 * 1 + 2 * 9 = 16 + 18 = 34. This satisfies the equation.
Therefore, the values of m and n that satisfy the equation are m = 1 and n = 9.
3 ways:
1. convert all 3 numbers to base 10, add them , then convert back
2. stay in base 2 by using the base 2 addition chart
+ 0 1
0 0 1
1 1 10
3. make use of this little applet
www.rapidtables.com/convert/number/base-converter.html
4. If using unix or its variants, use the program bc, and give it the commands
ibase=2
obase=2
and all your input and output will be in base 2