Maxim MAX12527 manual Binary-to-Gray and Gray-to-Binary Code Conversion

Dual, 65Msps, 12-Bit, IF/Baseband ADC

BINARY-TO-GRAY CODE CONVERSION															GRAY-TO-BINARY CODE CONVERSION
1) THE MOST SIGNIFICANT GRAY-CODE BIT IS THE SAME															1) THE MOST SIGNIFICANT BINARY BIT IS THE SAME AS THE
AS THE MOST SIGNIFICANT BINARY BIT.															MOST SIGNIFICANT GRAY-CODE BIT.
		D11				D7				D3			D0	BIT POSITION			D11				D7				D3			D0	BIT POSITION
	0		1	1	1	0	1	0	0	1	1	0	0	BINARY		0		1	0	0	1	1	1	0	1	0	1	0	GRAY CODE
	0													GRAY CODE		0													BINARY
2) SUBSEQUENT GRAY-CODE BITS ARE FOUND ACCORDING															2) SUBSEQUENT BINARY BITS ARE FOUND ACCORDING TO
TO THE FOLLOWING EQUATION:															THE FOLLOWING EQUATION:
	GRAYX = BINARYX +					BINARYX + 1										BINARYX = BINARYX+1					+	GRAYX
WHERE	+		IS THE EXCLUSIVE OR FUNCTION (SEE TRUTH												WHERE	+		IS THE EXCLUSIVE OR FUNCTION (SEE TRUTH
TABLE BELOW) AND X IS THE BIT POSITION:															TABLE BELOW) AND X IS THE BIT POSITION:
	GRAY10 = BINARY10					+	BINARY11									BINARY10 = BINARY11					+	GRAY10
	GRAY10 = 1 +				0											BINARY10 = 0				+ 1
	GRAY10 = 1															BINARY10 = 1
		D11				D7				D3			D0	BIT POSITION			D11				D7				D3			D0	BIT POSITION
0	+		1	1	1	0	1	0	0	1	1	0	0	BINARY	0			1	0	0	1	1	1	0	1	0	1	0	GRAY CODE
																+
0			1											GRAY CODE	0			1											BINARY
3) REPEAT STEP 2 UNTIL COMPLETE:															3) REPEAT STEP 2 UNTIL COMPLETE:
	GRAY9 = BINARY9 +					BINARY10										BINARY9 = BINARY10					+	GRAY9
	GRAY9 = 1			+	1
																BINARY9 = 1				+ 0
	GRAY9 = 0
																	BINARY9 = 1
														BIT POSITION															BIT POSITION
		D11				D7				D3			D0				D11				D7				D3			D0
0	1		+	1	1	0	1	0	0	1	1	0	0	BINARY	0	1			0	0	1	1	1	0	1	0	1	0	GRAY CODE
																		+
0	1			0										GRAY CODE	0	1			1										BINARY
4) THE FINAL GRAY-CODE CONVERSION IS:															4) THE FINAL BINARY CONVERSION IS:
		D11				D7				D3			D0	BIT POSITION			D11				D7				D3			D0	BIT POSITION
	0		1	1	1	0	1	0	0	1	1	0	0	BINARY		0		1	0	0	1	1	1	0	1	0	1	0	GRAY CODE
	0		1	0	0	1	1	1	0	1	0	1	0	GRAY CODE		0		1	1	1	0	1	0	0	1	1	0	0	BINARY

		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 MAX12527 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

MAX12527

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