Answer: Choice 'B' 10111₂
Explanation:
Binary numbers are similar to decimal numbers but they have a few differences. Binary are base 2 numbers, while decimal numbers such as 23 are in base 10. Another difference is binary are only in 1s and 0s, while decimals numbers go from 0-9.
So when decimal numbers go 1s place, 10s place, 100s place, (etc.), binary numbers go 1s place, 2s place, 4s place, (etc.).
We are trying to find the binary number the converts to 23. Let's look at each of the options.
Choice A: (1·1)+(2·1)+(4·0)+(8·0)+(16·1)=1+2+16=19
Choice B: (1·1)+(2·1)+(4·1)+(8·0)+(16·1)=1+2+4+16=23
Choice C: (1·1)+(2·0)+(4·1)+(8·0)+(16·1)=1+4+16=21
Choice D: (1·1)+(2·1)+(4·1)+(8·1)+(16·1)=1+2+4+8+16=31
For B, in the 1s place there was a 1, & (1·1)=1, in the 2s place there was a 2, & (2·1)=2, in the 4s place there was a 1, & (4·1)=4, in the 8s place there was a 0, & (8·0)=0 and in the 16s place there was a 1, & (16·1)=16.
From there I added all of the values together and got 23.
If you want to convert a decimal number to a binary number, there is a different process. It's a lot like long division, except with 1s & 0s and a base 2 number system.
Hope that helped a lot. Let me know any further questions.
:)