Digital computers do not "know" numbers the way humans do. Inside a CPU there are only two states — ON and OFF, represented as 1 and 0. Every calculation your computer performs — from a bank balance to a game score — is ultimately built from adding, subtracting, multiplying and dividing these binary digits, and from clever ways of encoding negative numbers using only 0s and 1s. This lesson teaches you exactly how that works.
For BCS, Bank IT, and IT-officer exams this is one of the highest-yield topics in Digital Logic Design. Questions on binary addition, 1's/2's complement, signed-number range, and overflow appear again and again. Master this and you can answer them mechanically and correctly, every time.
Learning objectives
- Add, subtract, multiply and divide numbers directly in binary.
- Understand the three signed representations: sign-magnitude, 1's complement, and 2's complement.
- Convert any signed number to and from decimal in each representation.
- Perform subtraction using 2's complement addition — the method real CPUs use.
- Detect and explain overflow and the carry vs. overflow distinction.
- State the exact range of values for an n-bit signed number.
- Avoid the classic exam traps that cost easy marks.