QQuestionMathematics
QuestionMathematics
Convert from binary to decimal numbers:
a. 1010100
b. 1101.001
c. 0.110011
10 months agoReport content
Answer
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Step 1:I'll solve this binary to decimal conversion problem step by step, following the specified LaTeX formatting guidelines:
Converting $$1010100_{2}$$ to decimal:
a.
Step 2:: Write out the place values from right to left
1010100_{2} = (1 \times 2^{6}) + (0 \times 2^{5}) + (1 \times 2^{4}) + (0 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (0 \times 2^{0})
Step 3:: Calculate each term
- $$0 \times 2^{0} = 0 \times 1 = 0
- 0 \times 2^{5} = 0 \times 32 = 0
Step 4:: Sum the values
64 + 0 + 16 + 0 + 4 + 0 + 0 = 84
Final Answer
b. Converting 1101.001_{2} to decimal: Step 1: Separate integer and fractional parts Integer part: 1101_{2} Fractional part: 0.001_{2} Step 2: Convert integer part 1 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 8 + 4 + 0 + 1 = 13 Step 3: Convert fractional part 0 \times 2^{- 1} + 0 \times 2^{- 2} + 1 \times 2^{- 3} = 0 + 0 + \frac{1}{8} = 0.125 Step 4: Combine parts 13 + 0.125 = 13.125 c. Converting 0.110011_{2} to decimal: Step 1: Calculate each fractional place value 1 \times 2^{- 1} + 1 \times 2^{- 2} + 0 \times 2^{- 3} + 0 \times 2^{- 4} + 1 \times 2^{- 5} + 1 \times 2^{- 6} Step 2: Compute values - 1 \times 2^{- 1} = 0.5 - 1 \times 2^{- 2} = 0.25 - 0 \times 2^{- 3} = 0 - 0 \times 2^{- 4} = 0 - 1 \times 2^{- 5} = 0.03125 - 1 \times 2^{- 6} = 0.015625 Step 3: Sum the values 0.5 + 0.25 + 0 + 0 + 0.03125 + 0.015625 = 0.796875
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