Binary Logic — Chapter Summary
NIOS · Class 12 · Computer Science
Summary of Binary Logic for NIOS Class 12 Computer Science. Part of the NIOS Class 12 Computer Science syllabus.
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Overview
Binary Logic is the fundamental foundation of all digital computing systems. It works exclusively with two states represented by 0 (false) and 1 (true), which align perfectly with how electronic circuits operate using ON/OFF states. This chapter explores how computers represent and process all types
Key Concepts
The binary number system uses only
The binary number system uses only two digits: 0 and 1. It has a base of 2, meaning each position represents a power of 2. For example, the binary num
The octal number system uses 8
The octal number system uses 8 digits: 0, 1, 2, 3, 4, 5, 6, 7. It has a base of 8. Each position represents a power of 8. For example, octal 23 = (2×8
The hexadecimal number system uses 16
The hexadecimal number system uses 16 digits: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). It has a base of 16, with each position represen
Converting between number systems is
Converting between number systems is a fundamental skill. Decimal to binary uses successive division by 2, recording remainders. For example, 9 ÷ 2 =
One's complement is obtained by inverting
One's complement is obtained by inverting all bits in a binary number—changing all 0s to 1s and all 1s to 0s. For example, the one's complement of 110
Learning Objectives
- Define and understand binary, octal, and hexadecimal number systems and their relationship to decimal numbers
- Convert numbers between different number systems (decimal to binary, binary to decimal, decimal to hexadecimal, etc.)
- Understand one's complement and two's complement representation of binary numbers for negative values
- Learn character coding systems (ASCII, ISCII, and Unicode) used by computers to represent text and symbols
- Identify and understand logic gates (AND, OR, NOT, NAND, NOR) and their truth tables
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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