Binary Addition and Subtraction With Negative Numbers, 2's Complements & Signed Magnitude 

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0:30 Worked example 1 - Writing -6 as a number using the signed magnitude method (4 bit binary) 1:55 Worked example 2 - Writing -7, -12, -15 using the signed magnitude method (5 bit binary) 2:43 Converting +7 in binary to -7 6:00 Expressing negative numbers using the 2's complement method 7:25 How to check your negative binary calculations in 2's complement 7:48 Worked example 3: -12 as a binary 2's complement number 9:50 Binary subtraction 2 ways - subtraction and 2's complement 12:05 2's Complement Subtraction 12:55 Changing +25 into -25 using the 2's complement method 15:30 What to do with a carry over / overflow number 16:34 Worked example 4: Subtracting 2 binary numbers 18:45 What to do when you can't borrow 19:52 Subtracting with the 2's Complement Method (by adding!)

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A helpful tip for finding the 2's compliment: flipping all of the bits and then adding 1 is the same as starting from the rightmost 1 and flipping all the bits higher than that.

Thank you for the info at 9:38; I could not understand how to do -7 +(-5) in 2s compliment until you showed that you just do the sign bit (-16) + all the ones.

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If you need to convert a binary number to its two’s complement form, you can use the method indicated by the video but there is a quicker method. For this you start at the least significant bit and move left ignoring any zeros up to the first 1, which you also ignore. Change any remaining bits from 0 to 1 or from 1 to 0. For example, expressing the number 10100100 in two’s complement form leaves the right-hand 100 unchanged, then the remaining 10100 changes to 01011, so the result is 01011100. ------------------------------ Edit: For negative numbers, Convert the positive version of the number to 2's complement and then, just add a "1" to the right of the most significant bit. Just adding 1 converts a two's complement to negative. DONE! Example: 2's complement of 12 ----> 0100 2"s complement of -12 -----> 10100 See there is an extra 1 at the right end. ------------------------------------------- Extra note: While 2's complement of 12 is 0100, it can be written as 0000000000100, u can have many 0s at the right end But for 2's complement of -12 is 10100, you cannot write it as 0010100, u gotta write it like 1111110100. See what I did there? 1 is the default right end of negative binary numbers, 0 is the default right end of positive binary numbers ( talking in terms of two's complement)

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9:11 video, Theres a shorter way we can do it, like consider the last digit of the 5th bit as "-16" and then just do regular algerba, i.e -16+4= -12 , SO set "16"and "4" as "1" and the rest "0" since we didnt use others. IN BINARY it will be 10100 . TRY THIS!

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you can also flip in parallel bitwise to it's bijective form and you can deduce certain things in parallel and make many more deductions about numbers.

Why did we have to use a 5 bit system when we can use a 4 bit system, when you expressed negative 6, the most significant bit had a zeor in it (0110) so we can just add 1 in the beginning(1110) to be negative 6, it should be the same when dealing with a 7 right? Since its(0111) we can just add a 1 in the most significant bit which represents the sign to be (1111)...and that should be a negative 7. Right?

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