To determine which of the given binary numbers is the largest, we can convert each binary number to its decimal (base-10) equivalent.
A. 11000000
- \(1 \times 2^7 + 1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 0 \times 2^0\)
- = \(128 + 64 + 0 + 0 + 0 + 0 + 0 + 0 = 192\)
B. 01111111
- \(0 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
- = \(0 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127\)
C. 00000001
- \(0 \times 2^7 + 0 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\)
- = \(0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1\)
D. 10111111
- \(1 \times 2^7 + 0 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
- = \(128 + 0 + 32 + 16 + 8 + 4 + 2 + 1 = 191\)
Now we can summarize the decimal values:
- A: 192
- B: 127
- C: 1
- D: 191
The largest binary number among the options is A. 11000000, which is equal to 192 in decimal.