Question

If the host address is 7.7.10.1\19 what is the broadcast address?

Answer 1

IP Address: 7.7.10.1
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Let's first convert this into binary format
7.7.10.1
Let's convert all octets to binary separately
Converting 7 to binary
Divide 7 successively by 2 until the quotient is 0
7/2 = 3, remainder is 1
3/2 = 1, remainder is 1
1/2 = 0, remainder is 1
Read remainders from the bottom to top as 111
7 in binary is 00000111

Converting 7 to binary
Divide 7 successively by 2 until the quotient is 0
7/2 = 3, remainder is 1
3/2 = 1, remainder is 1
1/2 = 0, remainder is 1
Read remainders from the bottom to top as 111
7 in binary is 00000111

Converting 10 to binary
Divide 10 successively by 2 until the quotient is 0
10/2 = 5, remainder is 0
5/2 = 2, remainder is 1
2/2 = 1, remainder is 0
1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1010
10 in binary is 00001010

Converting 1 to binary
Divide 1 successively by 2 until the quotient is 0
1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1
1 in binary is 00000001

===============================================================================
||    7.7.10.1 in binary notation is 00000111.00000111.00001010.00000001    ||
===============================================================================

Subnet mask is /19

For Calculating broadcast ID, keep first 19 bits of 00000111.00000111.00001010.00000001 and set all remaining bits to 1.
so, broadcast ID in binary is 00000111.00000111.00011111.11111111
00000111.00000111.00011111.11111111:
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00000111.00000111.00011111.11111111
Let's convert all octets to decimal separately
Converting 00000111 to decimal
=> 00000111
=> 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+1x2^2+1x2^1+1x2^0
=> 0x128+0x64+0x32+0x16+0x8+1x4+1x2+1x1
=> 0+0+0+0+0+4+2+1
=> 7
00000111 in decimal is 7

Converting 00000111 to decimal
=> 00000111
=> 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+1x2^2+1x2^1+1x2^0
=> 0x128+0x64+0x32+0x16+0x8+1x4+1x2+1x1
=> 0+0+0+0+0+4+2+1
=> 7
00000111 in decimal is 7

Converting 00011111 to decimal
=> 00011111
=> 0x2^7+0x2^6+0x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 0x128+0x64+0x32+1x16+1x8+1x4+1x2+1x1
=> 0+0+0+16+8+4+2+1
=> 31
00011111 in decimal is 31

Converting 11111111 to decimal
=> 11111111
=> 1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+1x64+1x32+1x16+1x8+1x4+1x2+1x1
=> 128+64+32+16+8+4+2+1
=> 255
11111111 in decimal is 255

==================================================================================
||    00000111.00000111.00011111.11111111 in decimal notation is 7.7.31.255    ||
==================================================================================
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||    So, broadcast ID is 7.7.31.255    ||
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