主題 / GCSE / Computer Science / Data Representation Binary arithmetic, shifts and hexadecimal 邊玩邊學
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課程筆記 Binary addition Rules: 0+0 = 0; 0+1 = 1; 1+1 = 10 (write 0, carry 1); 1+1+1 = 11 (write 1, carry 1). Example: 0101 + 0011 = 1000 (5 + 3 = 8). Overflow : if the result needs more bits than are available (e.g. an 8-bit register gets a 9th bit), the extra bit is lost, giving a wrong answer.Adding unsigned values Adding unsigned values Operation Binary Denary 00000101 + 00000011 00001000 5 + 3 = 8 11111111 + 00000001 100000000 255 + 1 = 256 8-bit result after overflow 00000000 0; carry cannot fit
Binary shifts A left shift moves bits left, filling with 0s: it multiplies an unsigned value by 2 for each place, provided no significant bit is lost. 00001100 (12) shifted left 2 = 00110000 (48). A right shift moves bits right, filling with 0s: it divides by 2 (rounding down) for each place. 00001100 shifted right 1 = 00000110 (6). Bits shifted off the end are lost . Unsigned eight-bit shifts Unsigned eight-bit shifts Operation Bit pattern Value Original 00001100 12 Left one 00011000 24 Right one 00000110 6 Left two 00110000 48
Hexadecimal Hexadecimal (base 16) uses digits 0-9 and A-F (A=10 ... F=15).Binary to hex : split into 4-bit groups (nibbles). 1010 1111 → A F → AF. Hex to binary : convert each digit: 3C → 0011 1100.Hex to denary : 3C = 3×16 + 12 = 60. Denary to hex : 255 = FF.Four bits per hex digit Four bits per hex digit Hex digit Four bits Denary 3 0011 3 6 0110 6 A 1010 10 C 1100 12 F 1111 15
Why hex? Hex is shorter and easier for humans to read and write than long binary: colour codes (#FF0000), memory addresses, MAC addresses and error codes. 投影片 Sign up free to view the lesson slides
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練習題 免費預覽——33 題中的 8 題。註冊即可查看全部。 1. What base does hexadecimal use?
Easy 2. What is binary 1 + 1?
Easy 3. What does overflow mean?
Easy A the result is too big for the bits availableB the result is zeroC the result is negativeD the loop ends4. What is F in denary?
Easy 5. For an unsigned binary value, with no significant bit lost, what is the effect of a one-place left shift?
Easy A doubles the valueB halves the valueC adds 1D subtracts 16. What is 00000110 shifted left 1?
Easy A 00001100B 00000011C 00001010D 000010007. What is 00001000 shifted right 2?
Easy A 00000010B 00100000C 00000100D 000000018. What is 0011 + 0110 in binary?
Easy 更多題目 9. What is 1010 in hex?
Easy 10. What is 1111 in hex?
Easy 11. What is hex 1F in denary?
Easy 12. What is 10101111 in hex?
Medium 13. What is hex 3C in binary?
Medium A 00111100B 11000011C 00111101D 0011001114. What is 255 in hex?
Medium 15. What is 00000101 + 00000011?
Medium A 00001000B 00000110C 00001010D 0000011116. What is 11111111 + 00000001 in an 8-bit register?
Medium A 00000000 with an overflowB 100000000 storedC 11111110D 1111111117. Why are colour codes often written in hex?
Medium A it is a short way to write binary valuesB it is the only wayC it saves paperD it is binary18. What is 00110000 shifted right 3?
Medium A 00000110B 00011000C 01100000D 0000001119. What is hex 7F in denary?
Medium 20. What is the largest unsigned value represented by a two-digit hexadecimal number?
Medium 21. For an unsigned binary value, with no significant bit lost, what is the effect of a three-place left shift?
Medium A multiplies by 8B multiplies by 3C divides by 8D adds 3A 4 bitsB 8 bitsC 2 bitsD 16 bits23. What does 'carry' mean?
Easy A a digit moved to the next columnB a loopC an errorD a variable24. What is 1100 in denary?
Medium 25. What is hex 10 in denary?
Medium 26. Hexadecimal uses digits 0-9 and A-F.
Easy True or false?
27. For an unsigned binary value, a one-place left shift doubles the value if no significant bit is lost.
Easy True or false?
28. A one-place logical right shift multiplies an unsigned binary value by 2.
Easy True or false?
29. Hex is easier for humans to read than long binary.
Easy True or false?
30. Overflow never causes errors.
Medium True or false?
A F in hexB 1111 in binaryC 00001111D 0F in hexE 1F in hex32. Which are uses of hex?
Medium A colour codesB memory addressesC MAC addressesD error codesE counting cats only33. Convert the binary number 01101011 to hexadecimal.
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