To solve the subtraction [tex]$(100100)_2 - (11010)_2$[/tex], we will follow these steps:
1. Convert the binary numbers to decimal (base 10):
- For the binary number [tex]\(100100_2\)[/tex]:
[tex]\[
100100_2 = 1 \cdot 2^5 + 0 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 0 \cdot 2^0
= 1 \cdot 32 + 0 \cdot 16 + 0 \cdot 8 + 1 \cdot 4 + 0 \cdot 2 + 0 \cdot 1
= 32 + 0 + 0 + 4 + 0 + 0
= 36
\][/tex]
- For the binary number [tex]\(11010_2\)[/tex]:
[tex]\[
11010_2 = 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0
= 1 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 0 \cdot 1
= 16 + 8 + 0 + 2 + 0
= 26
\][/tex]
2. Perform the subtraction in decimal:
- Subtract the converted numbers:
[tex]\[
36 - 26 = 10
\][/tex]
3. Convert the result back to binary (base 2):
- To convert 10 from decimal to binary:
[tex]\[
10 / 2 = 5 \quad \text{(remainder 0)}
\][/tex]
[tex]\[
5 / 2 = 2 \quad \text{(remainder 1)}
\][/tex]
[tex]\[
2 / 2 = 1 \quad \text{(remainder 0)}
\][/tex]
[tex]\[
1 / 2 = 0 \quad \text{(remainder 1)}
\][/tex]
Reading the remainders in reverse order, we get:
[tex]\[
10_{10} = 1010_2
\][/tex]
So, the detailed steps show that:
[tex]\( (100100)_2 - (11010)_2 = (1010)_2 \)[/tex]
Hence, the result of subtracting the binary numbers [tex]\( 100100_2 \)[/tex] and [tex]\( 11010_2 \)[/tex] is [tex]\( 1010_2 \)[/tex], which corresponds to 10 in decimal notation.
