The base 10 number 43 is represented as [____] in Binary.

Question

BlackTom AI · Accepted Answer

Convert 43 to binary by repeatedly dividing by 2 and recording remainders (least significant bit first).

Relevant concepts:
- Binary (base-2) uses digits 0 and 1, with place values 2^0, 2^1, 2^2, ...
- To convert a positive integer to binary, divide by 2 repeatedly and take remainders; read remainders from last to first to get the binary number.
- Each binary digit corresponds to whether that power of two is present (1) or absent (0).

Step-by-step division and intermediate remainders:
1) 43 ÷ 2 = 21 remainder 1 → least significant bit (LSB) = 1
2) 21 ÷ 2 = 10 remainder 1 → next bit = 1
3) 10 ÷ 2 = 5  remainder 0 → next bit = 0
4) 5  ÷ 2 = 2  remainder 1 → next bit = 1
5) 2  ÷ 2 = 1  remainder 0 → next bit = 0
6) 1  ÷ 2 = 0  remainder 1 → most significant bit (MSB) = 1

Reading the remainders from step 6 down to step 1 gives: 1 0 1 0 1 1, i.e., 101011 (binary).

Verification by place-value sum:
101011₂ = 1·2^5 + 0·2^4 + 1·2^3 + 0·2^2 + 1·2^1 + 1·2^0
= 1·32 + 0·16 + 1·8 + 0·4 + 1·2 + 1·1
= 32 + 0 + 8 + 0 + 2 + 1 = 43 (decimal).

Why this is correct and others are not:
- Binary representations are unique (without leading zeros). Any other 6-bit pattern yields a different decimal value: for example, 101010₂ = 32+0+8+0+2+0 = 42, and 101100₂ = 32+0+8+4+0+0 = 44. Thus 101011₂ is the only 6-bit pattern equal to 43.
- Leading zeros like 0101011 represent the same numeric value but are not the canonical minimal-length representation.

Conclusion: The base‑10 number 43 is correctly represented in binary as 101011, which matches the provided answer.

The base 10 number 43 is represented as [____] in Binary.Short answer

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