Let's go through the options one by one to determine which rules are correct for binary arithmetic:
1. [tex]$1 + 0 = 10$[/tex]
- This is incorrect. In binary arithmetic, [tex]$1 + 0$[/tex] is equal to [tex]$1$[/tex], not [tex]$10$[/tex].
2. [tex]$1 + 1 = 10$[/tex]
- This is correct. In binary arithmetic, when you add [tex]$1 + 1$[/tex], you get [tex]$10$[/tex]. This is because there is no digit '2' in binary; instead, the sum [tex]$1 + 1$[/tex] results in [tex]$0$[/tex] and carries over [tex]$1$[/tex] to the next higher bit, just like how [tex]$1 + 1 = 2$[/tex] in decimal results in a carry-over.
3. [tex]$1 \times 0 = 10$[/tex]
- This is incorrect. In binary arithmetic, [tex]$1 \times 0$[/tex] equals [tex]$0$[/tex], not [tex]$10$[/tex]. Multiplication in binary works similarly to decimal multiplication in this case.
4. [tex]$1 \times 1 = 1$[/tex]
- This is correct. In binary arithmetic, [tex]$1 \times 1$[/tex] equals [tex]$1$[/tex]. This rule is straightforward and is the same as in decimal arithmetic.
5. [tex]$1 - 0 = 0$[/tex]
- This is incorrect. In binary arithmetic, [tex]$1 - 0$[/tex] equals [tex]$1$[/tex]. This rule is also similar to subtraction in decimal arithmetic.
Therefore, the two correct rules for binary arithmetic are:
- [tex]$1 + 1 = 10$[/tex]
- [tex]$1 \times 1 = 1$[/tex]
