Consider the following input

ethereum yellow paper

Consider it's Keccak-256 hash according to this website:

7f110dc4c0a897ea5187a67e2c3a7db3a43410df8d1754fbdf28351c7e58400f

The first three pairs of bytes of Keccak-256 of an input string-

{7,f},{f,1},{1,0}

1. {7,f}

low order 11 bits of each of the first three pairs of bytes calculated using this website

00110111011

Its decimal equivalent calculated using this website is 777. 443%2048 = 443

Bloom filter will set a 443'th bit of 2048 bit sequence.

2. {f,1}

low order 11 bits of each of the first three pairs of bytes calculated using this website

01100110001

Its decimal equivalent calculated using this website is 817. 817%2048 = 817

Bloom filter will set a 817'th bit of 2048 bit sequence.

3. {1,0}

00110001001

low order 11 bits of each of the first three pairs of bytes calculated using this website

Its decimal equivalent calculated using this website is 393. 393%2048 = 393

Bloom filter will set a 393'th bit of 2048 bit sequence.

[i,i+1] denotes bytes at position i and i+1

Hope it helps!

Consider the following input

ethereum yellow paper

Consider it's Keccak-256 hash according to this website:

7f110dc4c0a897ea5187a67e2c3a7db3a43410df8d1754fbdf28351c7e58400f

The first three pairs of bytes of Keccak-256 of an input string-

{7,f},{f,1},{1,0}

1. {7,f}

low order 11 bits of each of the first three pairs of bytes calculated using this website

00110111011

Its decimal equivalent calculated using this website is 443. 443%2048 = 443

Bloom filter will set a 443'th bit of 2048 bit sequence.

2. {f,1}

low order 11 bits of each of the first three pairs of bytes calculated using this website

01100110001

Its decimal equivalent calculated using this website is 817. 817%2048 = 817

Bloom filter will set a 817'th bit of 2048 bit sequence.

3. {1,0}

00110001001

low order 11 bits of each of the first three pairs of bytes calculated using this website

Its decimal equivalent calculated using this website is 393. 393%2048 = 393

Bloom filter will set a 393'th bit of 2048 bit sequence.

[i,i+1] denotes bytes at position i and i+1

Hope it helps!

Consider the following input

ethereum yellow paper

Consider it's Keccak-256 hash according to this website:

a9c845160769c6f31dcbb1a4eea75cfa53461f12602b664ecb6dec596ae1b740

The first three pairs of bytes of Keccak-256 of an input string-

{a,9},{9,c},{c,8}

low order 11 bits of each of the first three pairs of bytes calculated using this website

1. {a,9}

01100001001

Its decimal equivalent calculated using this website is 777. 777%2048 = 777

Bloom filter will set a 777'th bit of 2048 bit sequence.

2. {9,c}

00111001011

Its decimal equivalent calculated using this website is 459. 459%2048 = 459

Bloom filter will set a 459'th bit of 2048 bit sequence.

3. {c,8}

01100011001

Its decimal equivalent calculated using this website is 793. 793%2048 = 793

Bloom filter will set a 793'th bit of 2048 bit sequence.

[i,i+1] denotes bytes at position i and i+1

Hope it helps!

Consider the following input

ethereum yellow paper

Consider it's Keccak-256 hash according to this website:

7f110dc4c0a897ea5187a67e2c3a7db3a43410df8d1754fbdf28351c7e58400f

The first three pairs of bytes of Keccak-256 of an input string-

{7,f},{f,1},{1,0}

1. {7,f}

low order 11 bits of each of the first three pairs of bytes calculated using this website

00110111011

Its decimal equivalent calculated using this website is 777. 443%2048 = 443

Bloom filter will set a 443'th bit of 2048 bit sequence.

2. {f,1}

low order 11 bits of each of the first three pairs of bytes calculated using this website

01100110001

Its decimal equivalent calculated using this website is 817. 817%2048 = 817

Bloom filter will set a 817'th bit of 2048 bit sequence.

3. {1,0}

00110001001

low order 11 bits of each of the first three pairs of bytes calculated using this website

Its decimal equivalent calculated using this website is 393. 393%2048 = 393

Bloom filter will set a 393'th bit of 2048 bit sequence.

[i,i+1] denotes bytes at position i and i+1

Hope it helps!