What is the decimal equivalent of 1100111 - 101001

1100111 --> 103

101001 --> 41

111110 --> 62

Explanation:

For this let's perform the subtraction operation to get the result.  Then, we will convert everything to decimal to check our work.

  0110 0111

-  0010 1001

  0011 1110

Now that we have performed the binary subtraction (using the same methods that you use for decimal subtraction), let's convert these numbers to their decimal forms.

0110 0111

= 0*2^7 + 1*2^6 + 1*2^5 + 0*2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 1*2^0

= 2^6 + 2^5 + 2^2 + 2^1 + 2^0

= 64 + 32 + 4 + 2 + 1

= 103

0010 1001

= 0*2^7 + 0*2^6 + 1*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 0*2^1 + 1*2^0

= 2^5 + 2^3 + 2^0

= 32 + 8 + 1

= 41

0011 1110

= 0*2^7 + 0*2^6 + 1*2^5 + 1*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 0*2^0

= 2^5 + 2^4 + 2^3 + 2^2 + 2^1

= 32 + 16 + 8 + 4 + 2

= 62

Now that we have done the conversion from binary to decimal, let's check that we performed the subtraction operation correctly.

103

- 41

62

Note, that 103-41 is indeed equal to 62.  Therefore, we have successfully performed the subtraction with the binary correctly.

Cheers.

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