3) The numbers 1 - 32 can be represented with a set of five
lights using the binary system. An "on" light is recorded with a
1, an "off" light is recorded with a 0. With the pattern given in the table, how would the number 23 be represented in 1's and
0's?
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- Each binary digit, or "bit", starting on the right side, is a power of 2, so the first bit is 20 = 1, the second is 21 = 2, and so on up to the 5th bit which is 24 = 16
- Here's how you turn a decimal number into binary:
- Write down the decimal number.
- Divide the number by 2.
- Write the result underneath.
- Write the remainder on the right hand side.
This will be 0 or 1.
- Divide the result of the division by 2 and again write down the remainder.
- Continue dividing and writing down remainders until the result of the division is 0.
The most significant bit (MSB) is at the bottom of the column of remainders and the least significant bit (LSB) is at the top.
Read the series of 1s and 0s on the right from the bottom up. This is the binary equivalent of the decimal number.
The binary representation of 23 is ______________
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