Задача Задача №1634009
А
А
310- 2 1010- .. 8 22610= ...16 б) 1102 + 112 = ...2 1102 - 112 = ...2 1102 × 112 = ...2 100012 = ...10 1748 = ...10 23C16 = ... 10 1102 :112= ...2 378 + 258= ...8 9C16 - 7816- ... 16
Let's convert and calculate the equations and numbers provided in your request systematically:
a)
310₈ to Base 10:
- \( 3 \times 8^2 + 1 \times 8^1 + 0 \times 8^0 = 3 \times 64 + 1 \times 8 + 0 = 192 + 8 + 0 = 200 \)
- 310₈ = 200₁₀
226₁₀ to Base 16:
- \( 226_{10} \div 16 \) gives quotient 14 (E) and remainder 2.
- Therefore, 226₁₀ = E2₁₆
b)
110₂ + 112₂:
- \(110_2\) = 6 in decimal, \(112_2\) = 3 in decimal.
- \(6 + 3 = 9\) in decimal = \(1001_2\).
- 110₂ + 112₂ = 1001₂
110₂ - 112₂:
- \(110_2 - 112_2\) = \(6 - 3 = 3\) in decimal = \(011_2\).
- 110₂ - 112₂ = 11₂
110₂ × 112₂:
- \(110_2 \times 11_2\) = \(6 \times 3 = 18\) in decimal.
- \(18_{10} = 10010_2\).
- 110₂ × 112₂ = 10010₂
10000₁₀ to Base 2:
- \(10000_{10} = 11000100000_2\).
- 10000₁₀ = 11000100000₂
1748 to Base 10:
- It is already in decimal.
- 1748 = 1748₁₀
23C₁₆ to Decimal:
- \(2 \times 16^2 + 3 \times 16^1 + C \times 16^0\) (where C is 12)
- \(2 \times 256 + 3 \times 16 + 12 = 512 + 48 + 12 = 572\)
- 23C₁₆ = 572₁₀
110₂ : 112₂:
- \(6 ÷ 3 = 2\) in decimal = \(10_2\).
- 110₂ : 112₂ = 10₂
c)
378 + 258 in Base 8:
- \(378_{10} + 258_{10} = 636_{10}\).
- To convert to octal (base 8): \(636 ÷ 8 = 79 R4\) , \(79 ÷ 8 = 9 R7\), \(9 ÷ 8 = 1 R1\), \(1 ÷ 8 = 0 R1\).
- Reading from bottom to top gives \(1144_8\).
- 378 + 258 = 1144₈
9C₁₆ - 78₁₆:
- Convert \(9C₁₆\) to decimal: \(9 \times 16^1 + 12 \times 16^0 = 144 + 12 = 156\).
- Convert \(78₁₆\) to decimal: \(7 \times 16^1 + 8 \times 16^0 = 112 + 8 = 120\).
- Subtract: \(156 - 120 = 36\).
- Convert \(36_{10}\) to hex: \(36 = 24_{16}\).
- 9C₁₆ - 78₁₆ = 24₁₆
Summary:
- 310₈ = 200₁₀
- 226₁₀ = E2₁₆
- 110₂ + 112₂ = 1001₂
- 110₂ - 112₂ = 11₂
- 110₂ × 112₂ = 10010₂
- 10000₁₀ = 11000100000₂
- 1748 = 1748₁₀
- 23C₁₆ = 572₁₀
- 110₂ : 112₂ = 10₂
- 378 + 258 = 1144₈
- 9C₁₆ - 78₁₆ = 24₁₆
