Binary Number System – AP CSP | ShowMeClass

01

Binary Number System

AP CSP · Unit 1: Digital Information

Learning Objectives

Convert between binary, decimal & hexadecimal

Understand place values in base-2

Explain how computers store numbers as bits

Calculate max value for N bits (2^N−1)

Key Concepts

Bit: Binary digit — 0 or 1

Byte: 8 bits (0–255)

Place Value: Each bit represents 2ⁿ where n is position from right (starting at 0)

Hexadecimal: Base-16 (0–F), compact representation of binary

Powers of 2

        20=1   21=2   22=4   23=8

        24=16   25=32   26=64   27=128

Colors

Active bit (1)

Inactive bit (0)

Contribution value

BinaryDecimalHex

Bits:8

Max Value:255

Used:0 / 8 bits

Binary

00000000

Decimal

0

Hexadecimal

0x00

Octal

0o000

Base Converter

Decimal

Binary

Hex

Number of Bits 8

Quick Values

Operations

Analysis

Quick Quiz▼

1. What is the decimal value of binary 1010?

8 10 12 5

2. How many values can 8 bits represent?

128 255 256 512

3. What is binary 11111111 in hexadecimal?

0xF0 0xFF 0x1F 0xFE