1.1 Number systems

By the end of this section you should be able to

• 1.1.1 Explain why computers use binary for all data
• 1.1.2 Convert between denary, binary and hexadecimal (up to 16-bit)
• 1.1.3 Explain why hexadecimal is used and where
• 1.1.4 Add two 8-bit binary integers and recognise overflow
• 1.1.5 Perform logical left and right shifts and describe their effect
• 1.1.6 Represent positive and negative integers in 8-bit two's complement

Lessons

1. Binary number system
2. Hexadecimal number system
3. Hexadecimal uses
4. Binary addition and overflow
5. Logical binary shifts
6. Negative binary numbers

Key vocabulary

Binary

A base 2 number system that uses only the digits 0 and 1.

Denary

A base 10 number system that uses the digits 0 to 9.

Hexadecimal

A base 16 number system that uses 0 to 9 and A to F; a shorter way to write binary.

Overflow error

Happens when a result is too large to fit in the register, e.g. above 255 in 8 bits.

Logical shift

Moving all bits left or right, losing bits off one end and filling with zeros at the other.

Two's complement

A method of representing negative binary integers. The leftmost bit is the sign bit, and you flip the bits and add 1 to change the sign.

Most significant bit

The leftmost bit in a binary number, with the highest place value.