Logic Lab
Number Systems
Bit, nibble, byte and word. Convert between binary, octal, decimal and hexadecimal, and see BCD and complements.
8-bit value, every reading
128
64
32
16
8
4
2
1
Type a number in base
Number systems
Binary0100 0001
Octal (8)101
Decimal (10)65
Hexadecimal (16)0x41
Signed representations
Unsigned65
Two’s complement65
One’s complement65
Codes
BCD (packed decimal)0110 0101
Gray code0110 0001
Gray decoded back126
Character (ASCII/Unicode)A
Character (EBCDIC)–
The same bits mean different things depending on how you read them. Two’s complement is what computers use for negatives: the top bit counts as −128. A group of 4 bits is a nibble, 8 bits a byte, and a word is however many bits the machine handles at once (here 8 bits = 2 nibbles = 1 bytes). Gray code changes one bit between neighbours, which is why Karnaugh maps use it. Typing in binary, octal, decimal or hex updates the switches live.