Math Problem Statement

Convert 1110010101

Solution

To convert the binary number 111001010121110010101_2 to decimal:

We use positional notation, where each digit is multiplied by 2n2^n, where nn is its position from right (starting at 0):

11100101012=1×29+1×28+1×27+0×26+0×25+1×24+0×23+1×22+0×21+1×201110010101_2 = 1 \times 2^9 + 1 \times 2^8 + 1 \times 2^7 + 0 \times 2^6 + 0 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0

Calculating:

=1×512+1×256+1×128+0×64+0×32+1×16+0×8+1×4+0×2+1×1= 1 \times 512 + 1 \times 256 + 1 \times 128 + 0 \times 64 + 0 \times 32 + 1 \times 16 + 0 \times 8 + 1 \times 4 + 0 \times 2 + 1 \times 1 =512+256+128+16+4+1=917= 512 + 256 + 128 + 16 + 4 + 1 = 917

So, 111001010121110010101_2 in decimal is **

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Math Problem Analysis

Mathematical Concepts

Binary Numbers
Positional Notation
Number Conversion

Formulas

Binary to Decimal Conversion Formula: Sum of digits times powers of 2

Theorems

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Suitable Grade Level

Grades 6-8