Maxim MAX12557 manual Binary-to-Gray and Gray-to-Binary Code Conversion

+ GRAYX

Dual, 65Msps, 14-Bit, IF/Baseband ADC

BINARY-TO-GRAY CODE CONVERSION

1)THE MOST SIGNIFICANT GRAY-CODE BIT IS THE SAME AS THE MOST SIGNIFICANT BINARY BIT.

D13		D11				D7				D3			D0	BIT POSITION
0	1	1	0	1	1	0	1	0	0	1	1	0	0	BINARY
0														GRAY CODE

2)SUBSEQUENT GRAY-CODE BITS ARE FOUND ACCORDING TO THE FOLLOWING EQUATION:

GRAYX = BINARYX + BINARYX + 1

WHERE + IS THE EXCLUSIVE OR FUNCTION (SEE TRUTH

TABLE BELOW) AND X IS THE BIT POSITION:

GRAY12 = BINARY12 + BINARY13

GRAY12 = 1 + 0

GRAY12 = 1

D13		D11	D7	D3	D0	BIT POSITION
0	+ 1	1 0 1 1	0 1 0 0	1	1 0 0	BINARY
0	1					GRAY CODE

3)REPEAT STEP 2 UNTIL COMPLETE: GRAY11 = BINARY11 + BINARY12 GRAY11 = 1 + 1

GRAY11 = 0

D13				D11			D7				D3			D0	BIT POSITION
0	1	+	1	0	1	1	0 1	0	0		1	1	0	0	BINARY
0	1		0												GRAY CODE
4) THE FINAL GRAY-CODE CONVERSION IS:
D13			D11				D7				D3			D0	BIT POSITION
0		1	1	0	1	1	0	1	0	0	1	1	0	0	BINARY
0		1	0	1	1	0	1	1	1	0	1	0	1	0	GRAY CODE

GRAY-TO-BINARY CODE CONVERSION

1)THE MOST SIGNIFICANT BINARY BIT IS THE SAME AS THE MOST SIGNIFICANT GRAY-CODE BIT.

D13		D11				D7				D3			D0
0	1	0	1	1	0	1	1	1	0	1	0	1	0
0

2)SUBSEQUENT BINARY BITS ARE FOUND ACCORDING TO THE FOLLOWING EQUATION:

BINARYX = BINARYX+1

WHERE + IS THE EXCLUSIVE OR FUNCTION (SEE TRUTH TABLE BELOW) AND X IS THE BIT POSITION:

BINARY12 = BINARY13 + GRAY12

BINARY12 = 0 + 1

BINARY12 = 1

D13		D11				D7				D3			D0
0	1	0	1	1	0	1	1	1	0	1	0	1	0
	+

01

3)REPEAT STEP 2 UNTIL COMPLETE:

BINARY11 = BINARY12 + GRAY11

BINARY11 = 1 + 0

BINARY11 = 1

D13			D11			D7				D3			D0
0	1	0	1	1	0	1	1	1	0	1	0	1	0
		+
0	1	1
4) THE FINAL BINARY CONVERSION IS:
D13		D11				D7				D3			D0
0	1	0	1	1	0	1	1	1	0	1	0	1	0
0	1	1	0	1	1	0	1	0	0	1	1	0	0

BIT POSITION GRAY CODE

BINARY

BIT POSITION GRAY CODE

BINARY

BIT POSITION

GRAY CODE

BINARY

BIT POSITION GRAY CODE

BINARY

MAX12557

		EXCLUSIVE OR TRUTH TABLE
FIGURE 8 SHOWS THE GRAY-TO-BINARY AND BINARY-TO-GRAY	A	B	Y = A + B
CODE CONVERSION IN OFFSET BINARY FORMAT. THE OUTPUT
FORMAT OF THE MAX12557 IS TWO'S-COMPLEMENT BINARY,	0	0	0
HENCE EACH MSB OF THE TWO'S-COMPLEMENT OUTPUT CODE	0	1	1
MUST BE INSERTED TO REFLECT TRUE OFFSET BINARY FORMAT.
	1	0	1
	1	1	0

Figure 8. Binary-to-Gray and Gray-to-Binary Code Conversion

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