What is the binary representation of the decimal number 147?

Study for the FAA-H-8083-30B AMT General Handbook – Mathematics in Aviation Maintenance Exam. Engage with flashcards and multiple choice questions, with hints and explanations. Get ready for your exam!

To determine the binary representation of the decimal number 147, we can break down the conversion process into clearer steps. The primary goal is to express the number 147 in base 2, which involves finding the powers of 2 that sum up to this decimal value.

Starting from the higher power of 2, we can identify the largest power of 2 less than or equal to 147, which is 128 (2^7). This indicates that the first binary digit (from the left) is a 1, representing this power. We then subtract 128 from 147, resulting in 19.

Continuing with 19, the next largest power of 2 is 16 (2^4). This means we add another 1 in the binary representation for this position. We then subtract 16 from 19, leaving us with 3.

Next, we identify the largest power of 2 in 3, which is 2 (2^1). We add a 1 in this position and subtract 2 from 3, leaving us with 1.

Finally, the number 1 is represented as 2^0, and we add a 1 in this position too.

After tallying the

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