The central processing unit

The CPU executes instructions. Its main parts are:

• Arithmetic and logic unit (ALU) — does calculations and logical comparisons.
• Control unit (CU) — directs the flow of data and decodes instructions.
• Registers — tiny, very fast stores inside the CPU.

Key registers: the program counter (PC) holds the address of the next instruction; the memory address register (MAR) holds the address being accessed; the memory data register (MDR) holds the data in transit; the accumulator holds results from the ALU.

Which register?

The machine instruction cycle

The CPU repeats the fetch to decode to execute cycle:

• Fetch — the instruction at the PC address is copied from memory; the PC then increments.
• Decode — the control unit works out what the instruction means.
• Execute — the ALU or CU carries it out; results go to the accumulator or memory.

Primary and secondary memory

Primary memory is directly accessible by the CPU:

• RAM — volatile, read and write, holds running programs and data.
• ROM — non-volatile, read-only, holds start-up firmware.
• Cache — very fast memory near the CPU that stores frequently used data.

Secondary storage (hard disk, SSD, USB drive, optical disc) is non-volatile, larger, slower and not directly addressable by the CPU.

Sort the storage

Tap an item, then the category it belongs to.

Binary and denary

Computers store everything in binary (base 2). Each bit is a power of two. In an 8-bit byte the place values are 128, 64, 32, 16, 8, 4, 2, 1.

Denary 156 = 128 + 16 + 8 + 4 = 1001 1100. To convert back, add the place values wherever a bit is 1.

Binary to denary

Denary to binary

Hexadecimal

Hexadecimal (base 16) is a short way to write binary. Digits run 0 to 9 then A to F (A=10 ... F=15). Each hex digit maps to exactly 4 bits.

Denary 220 = 13 remainder 12 in base 16, so 220 = D (13) then C (12) = DC. Check: 13 times 16 + 12 = 220.

Hex to denary

Denary to hex

Two’s complement

To store negative integers, computers use two’s complement. To find the pattern for a negative number in 8 bits: write the positive value in binary, invert all the bits, then add 1.

Minus 40: 40 = 0010 1000. Invert: 1101 0111. Add 1: 1101 1000. The leading 1 shows it is negative.

Two’s complement

Binary arithmetic and shifts

Binary addition works column by column, carrying when the total reaches 2 (10 in binary).

0101 1010 + 0010 1110 = 1000 1000 (90 + 46 = 136).

A logical left shift by n places moves every bit left and fills with zeros. Each single left shift multiplies by 2, so shifting left by 2 places multiplies by 4. A logical right shift by n divides by 2 to the power n (integer division).

Logical shift

Boolean logic gates

Digital circuits are built from logic gates. The core gates are:

• AND — output 1 only when both inputs are 1.
• OR — output 1 when at least one input is 1.
• NOT — inverts a single input.
• XOR — output 1 only when the inputs differ.
• NAND / NOR — AND / OR followed by a NOT (the output is inverted).

Match the logic gate

Tap a behaviour on the left, then the gate that produces it.

Volatile memory

The big ideas to know

You have covered the whole of Topic 2 — computer organisation. Press Finish to see your score.