1. (A1)₁₆ = (      ?      )_{Gray Code}

Solution:
(A1)₁₆ = (_______)_GrayCode

1. Convert hexadecimal to binary
(A1)₁₆ = (_______)₂

A	1
1010	0001

`:.` (A1)₁₆ = (10100001)₂


2. Convert binary to GrayCode
Binary code : `10100001`

Method-1: (Binary to Gray code)
`g_7=b_7=1`

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

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

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

`g_3=b_4 o+ b_3=0 o+ 0=0`

`g_2=b_3 o+ b_2=0 o+ 0=0`

`g_1=b_2 o+ b_1=0 o+ 0=0`

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

`:.` Gray code : `11110001`

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Method-2: (Binary to Gray code)

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

`:.` Gray code : `11110001`

`:.` (A1)₁₆ = (11110001)_GrayCode

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2. (123)₁₆ = (      ?      )_{Gray Code}

Solution:
(123)₁₆ = (_______)_GrayCode

1. Convert hexadecimal to binary
(123)₁₆ = (_______)₂

1	2	3
0001	0010	0011

`:.` (123)₁₆ = (100100011)₂


2. Convert binary to GrayCode
Binary code : `100100011`

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+ 0=0`

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

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

`g_3=b_4 o+ b_3=0 o+ 0=0`

`g_2=b_3 o+ b_2=0 o+ 0=0`

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

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

`:.` Gray code : `110110010`

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Method-2: (Binary to Gray code)

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

`:.` Gray code : `110110010`

`:.` (123)₁₆ = (110110010)_GrayCode

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