Answer to Question #226037 in Combinatorics | Number Theory for Minenhle Pelican C

Question

1.   Subtract the binary numbers 1110₂ from 10101₂

Answer 1

Let us subtract the binary numbers 1110₂ from 10101₂:

$10101_2\\ \ \ 1110_2\\ ---\\ \ \ \ \ 111_2$

Let us verify using decimal system:

$10101_2=1\cdot 2^4+0\cdot 2^3+1\cdot 2^2+0\cdot 2+1=16+4+1=21_{10} \\ 1110_2=1\cdot 2^3+1\cdot 2^2+1\cdot 2+0=8+4+2=14_{10}\\ 111_2=1\cdot 2^2+1\cdot 2+1=4+2+1=7_{10}$

And $14+7=21$

Answer: 111₂