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`

Method-2: (Binary to Gray code)

`b_8` `1`	`b_7` `0`	`b_6` `1`	`b_5` `0`	`b_4` `1`	`b_3` `1`	`b_2` `0`	`b_1` `0`	`b_0` `1`	Binary code
`b_8` `1`	`b_8 o+ b_7` `1 o+ 0`	`b_7 o+ b_6` `0 o+ 1`	`b_6 o+ b_5` `1 o+ 0`	`b_5 o+ b_4` `0 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+ 0`	`b_1 o+ b_0` `0 o+ 1`
`darr`	`darr`	`darr`	`darr`	`darr`	`darr`	`darr`	`darr`	`darr`
`1` `g_8`	`1` `g_7`	`1` `g_6`	`1` `g_5`	`1` `g_4`	`0` `g_3`	`1` `g_2`	`0` `g_1`	`1` `g_0`	Gray code

`:.` Gray code : `111110101`

`:.` (345)₁₀ = (111110101)_GrayCode

This material is intended as a summary. Use your textbook for detail explanation.
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