J 27602 Computational thinking algorithms and programming Computer

(J 276/02) Computational thinking, algorithms and programming Computer Science Theory: 2. 6 – Data Representation Binary Shift

Computational thinking, algorithms and programming Computer Science Binary Shift A binary shift (also known as a logical shift) is just as the name suggests; the shifting or moving of binary values to the left or the right. As we know, 8 bits are called a byte, which is the smallest addressable unit of memory. So, a binary shift is moving each bit in a defined direction (left or right). Since we work in bytes, any bits that fall out of that 8 bit block are lost forever. Multiply or divide by Shifts 2 = 21 1 4 = 22 2 8 = 23 3 16 = 24 4 32 = 25 5 64 = 26 6 128 = 27 7

Computational thinking, algorithms and programming Computer Science Left Shift Example: 3 x 8 128 0 64 0 32 0 16 0 8 0 To multiply by 8, we need to shift the binary digits to the left by 3 places. 128 0 0 64 0 0 32 0 0 16 0 1 16 4 0 2 1 1 1 2 x 2 x 2=8 8 0 1 +8 4 0 0 2 1 0 1 1 0 =24

Computational thinking, algorithms and programming Computer Science Practise Questions Write these out in binary: 1. 1111 x 4 = 2. 100001 x 2 = Convert to binary first: 3. 70 x 8 = Multiply or divide by Shifts 2 = 21 1 4 = 22 2 8 = 23 3 16 = 24 4 32 = 25 5 64 = 26 6 128 = 27 7

Computational thinking, algorithms and programming Computer Science Practise Questions Convert to binary first: 3. 70 x 8 = 01000110 x 8 = 00110000

Computational thinking, algorithms and programming Computer Science Right Shift Example: 192 ÷ 16 128 1 64 1 32 0 16 0 8 0 To divide by 16, we need to shift the binary digits to the right by 4 places. 128 1 0 64 1 0 32 0 0 16 0 0 4 0 2 0 1 0 2 x 2 x 2 = 16 8 0 1 4 0 1 8 +4 2 0 0 1 0 0 =12

Computational thinking, algorithms and programming Computer Science Practise Questions Multiply or divide by Shifts Write these out in binary: 2 = 21 1 4 = 22 2 1. 11001000 ÷ 8 8 = 23 3 16 = 24 4 32 = 25 5 64 = 26 6 128 = 27 7 2. 00010110 ÷ 2 = = Convert to binary first: 3. 224 ÷ 32 =

Computational thinking, algorithms and programming Computer Science Practise Questions Write these out in binary: 1. 11001000 ÷ 8 = 00011001 2. 00010110 ÷ 2 = 00001011 Convert to binary first: 3. 224 ÷ 32 = 11100000 ÷ 32 = 00000111

Computational thinking, algorithms and programming Computer Science Theory Plenary- Self Assessment Using WWW and EBI rate yourself against todays objectives: 1. To be able to demonstrate an understanding of binary shift calculations. Next theory lesson: Hexadecimal Conversions