Knowledge base

Bit-level variable representation

A variable can store not only a regular number, but also a set of separate flags. Industrial automation often packs states, alarms, permissions, operating modes and status flags into Modbus registers this way.

A bit as a separate flag

Each bit has a number and a weight. If the bit is 1, its weight is added to the final value. If the bit is 0, it adds nothing. For integer types this is a simple sum of powers of two.

Value = bit0 x 2⁰ + bit1 x 2¹ + bit2 x 2² + ... For example, if bits 0, 3 and 7 are enabled, the value is 1 + 8 + 128 = 137.

bit 72⁷128

bit 62⁶64

bit 52⁵32

bit 42⁴16

bit 32³8

bit 22²4

bit 12¹2

bit 02⁰1

BYTE, WORD and DWORD

BYTE contains 8 bits, WORD contains 16 bits, and DWORD contains 32 bits. In Modbus maps a 16-bit holding register is often described as a WORD: it can represent one value from 0 to 65535 or 16 independent flags.

Type	Size	Typical use
`BYTE`	8 bits	Small flag set or a value from 0 to 255.
`WORD`	16 bits	One Modbus register, status word, alarm word, control word.
`DWORD`	32 bits	Two Modbus registers, a larger flag mask or a 32-bit value.

Signed types

In SHORT8, INT16 and DINT32, the highest bit participates in signed representation. Two's complement is typically used: if the highest bit is set, the number is negative. For example, an INT16 bit pattern 1111 1111 1111 1111 means -1, not 65535.

REAL: sign, exponent and mantissa

REAL is not a simple sum of bits. In most PLC and SCADA systems it is stored as a 32-bit IEEE-754 Float32 value: one sign bit, 8 exponent bits and 23 mantissa bits. The same 32 bits can be interpreted as UDINT32 or as REAL, but the meaning is different.

bit number	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
part	MANTISSA
content	1/2¹	1/2²	1/2³	1/2⁴	1/2⁵	1/2⁶	1/2⁷	1/2⁸	1/2⁹	1/2¹⁰	1/2¹¹	1/2¹²	1/2¹³	1/2¹⁴	1/2¹⁵	1/2¹⁶
bit value	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

bit number	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
part	MANTISSA							EXPONENT								S
content	1/2¹⁷	1/2¹⁸	1/2¹⁹	1/2²⁰	1/2²¹	1/2²²	1/2²³	2⁰	2¹	2²	2³	2⁴	2⁵	2⁶	2⁷	+/-
bit value	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Formula(-1)^S x 1.M x 2^E-127

MantissaThe fractional part. In a normalized REAL value, an implicit leading one is used: 1.M.

ExponentStored with a bias of 127. If the exponent field is 127, the real power is 0.

Sign0 means positive, 1 means negative.

What matters in Modbus

Modbus transfers 16-bit registers. If a variable occupies 32 bits, it is stored in two registers. For DWORD, DINT32 and REAL, word order matters: high word first or low word first. If the order is wrong, the bits are the same, but the decoded value is wrong.

Practice For quick checks, use the bit calculator: choose a type, toggle bits or paste a HEX value from a register.