Conquer Computer Science: Data Representation (Part 3/5)

Explore the denary decimal number system with base ten digits 0–9 and positional notation, where place value drives calculations and computers use a similar but more complex system.

Explore how computers use binary, two-state electrical switches to represent numbers with bits and bytes, including kilobytes vs kibibytes and base-two vs base-ten grouping.

Master binary-denary conversions by identifying place values, doubling powers of two, and using both direct and division methods to translate eight-bit and variable-length binaries into denary.

Learn how binary addition works like regular arithmetic, with carries and overflow in eight-bit registers, and see how the CPU performs repeated additions and manages overflow.

Discover how binary shifts multiply and divide by two. Use left shifts to multiply and right shifts to divide, and note overflow and floor division in binary and denary contexts.

Learn how two's complement represents negative binary numbers using the sign bit, flipping bits, and adding one. See how 81 and -33 illustrate eight-bit limits in practical examples.

Learn how hexadecimal, a base-16 system using digits 0-9 and A-F, makes reading binary switches easier and represents bytes with two-digit hex in colors, mac addresses, ipv6, and text.

Explore reading and converting hexadecimal and denary numbers, using place values, repeated division by 16, and nibble-based binary conversion, with practice questions.

Learn how ascii and unicode encode letters and symbols as numeric codes using binary and hexadecimal, including euro and emojis encoded in up to four bytes for consistent text display.

Learn how computers represent images with vector graphics and raster bitmaps, using shapes and equations or colored pixels, and explore formats like SVG, JPEG, PNG, and GIF.

Learn how computers convert analog sound into digital data by sampling amplitude at regular intervals, using bits and sampling rate to balance quality and file size.

Video digitizes as a series of still images shown at 20–60 fps with audio on separate tracks, encoded by MP4 from MPEG and JPEG from the Joint Photographic Experts Group.

Explore how computers store data as bits and bytes, including on/off electrical states and magnetic representations, and compare text, image, and audio file sizes from kilobyte to exbibyte.

Explore data compression, comparing lossy and lossless methods, with examples like jpeg, mp3, mp4, png, and rl encoding, to understand irreversible data loss vs reversible redundancy elimination for smaller files.

Explore how boolean algebra and boolean logic translate binary digits into electrical switches powering computers. See how and, or, not, nand, nor, xor operators map inputs to outputs in circuits.

Explore the building blocks of computers through logic gates such as not, and, or, nand, nor, and xor. See how truth tables map inputs to ones and zeros in circuits.

Visualize the shapes of these logic gates to remember them. Create vivid images for each gate: not as a bow-tie with a knot, or as a rowboat, XOR with ripples.

Combine logic gates into circuits to create memory with gated latches or flip-flops. Build half and full adders using xor gates and and/or gates.

Test logic circuits with truth tables that map binary inputs, 1 and 0, to outputs. Structure tables for multiple inputs and intermediate steps to compare expressions and their equivalence.

Explore how logic expressions, truth tables, and circuit diagrams interconvert, using boolean algebra to express conditions with inputs A, B, and C through xor and gates.

Explore courses on hardware and software, binary data representation of images, videos, and sounds, and data transmission across the internet and the web.