Decimal To Gray Code converter Examples

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Home > Pre-Algebra calculators > Decimal To Gray code conversion example

Decimal To Gray Code converter example ( Enter your problem )

( Enter your problem )

Examples

Other related methods

1. Examples

1. (123)₁₀ = ( ? )_{Gray Code}

Solution:
(123)₁₀ = (_______)_GrayCode

1. Convert decimal to binary
(123)₁₀ = (_______)₂

2	123
2	61	1	↑
2	30	1	↑
2	15	0	↑
2	7	1	↑
2	3	1	↑
2	1	1	↑
	0	1	↑

$:.$ (123)₁₀ = (1111011)₂

2. Convert binary to GrayCode
Binary code : $1111011$

Method-1: (Binary to Gray code)

$g_6=b_6=1$

$g_5=b_6 o+ b_5=1 o+ 1=0$

$g_4=b_5 o+ b_4=1 o+ 1=0$

$g_3=b_4 o+ b_3=1 o+ 1=0$

$g_2=b_3 o+ b_2=1 o+ 0=1$

$g_1=b_2 o+ b_1=0 o+ 1=1$

$g_0=b_1 o+ b_0=1 o+ 1=0$

$:.$ Gray code : $1000110$

Method-2: (Binary to Gray code)

$b_6$ $1$	$b_5$ $1$	$b_4$ $1$	$b_3$ $1$	$b_2$ $0$	$b_1$ $1$	$b_0$ $1$	Binary code
$b_6$ $1$	$b_6 o+ b_5$ $1 o+ 1$	$b_5 o+ b_4$ $1 o+ 1$	$b_4 o+ b_3$ $1 o+ 1$	$b_3 o+ b_2$ $1 o+ 0$	$b_2 o+ b_1$ $0 o+ 1$	$b_1 o+ b_0$ $1 o+ 1$
$darr$	$darr$	$darr$	$darr$	$darr$	$darr$	$darr$
$1$ $g_6$	$0$ $g_5$	$0$ $g_4$	$0$ $g_3$	$1$ $g_2$	$1$ $g_1$	$0$ $g_0$	Gray code

$:.$ Gray code : $1000110$

$:.$ (123)₁₀ = (1000110)_GrayCode

2. (345)₁₀ = ( ? )_{Gray Code}

Solution:
(345)₁₀ = (_______)_GrayCode

1. Convert decimal to binary
(345)₁₀ = (_______)₂

2	345
2	172	1	↑
2	86	0	↑
2	43	0	↑
2	21	1	↑
2	10	1	↑
2	5	0	↑
2	2	1	↑
2	1	0	↑
	0	1	↑

$:.$ (345)₁₀ = (101011001)₂

2. Convert binary to GrayCode
Binary code : $101011001$

Method-1: (Binary to Gray code)

$g_8=b_8=1$

$g_7=b_8 o+ b_7=1 o+ 0=1$

$g_6=b_7 o+ b_6=0 o+ 1=1$

$g_5=b_6 o+ b_5=1 o+ 0=1$

$g_4=b_5 o+ b_4=0 o+ 1=1$

$g_3=b_4 o+ b_3=1 o+ 1=0$

$g_2=b_3 o+ b_2=1 o+ 0=1$

$g_1=b_2 o+ b_1=0 o+ 0=0$

$g_0=b_1 o+ b_0=0 o+ 1=1$

$:.$ Gray code : $111110101$