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