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京都大学 情報学研究科 通信情報システム専攻 2020年8月実施 専門基礎A [A-7]

Author​

SUN

Description​

Answer all the following questions.

(1) Answer the following questions on the binary number representation.
  (a) Express the following decimal numbers in the 8-bit two’s complement representation.
    (i) +88     (ii) −72

  (b) Convert the following 8-bit two’s complement binary numbers into the 8-bit sign-and-magnitude binary representation.
    (i) 10101010     (ii) 11010101

  (c) Show the results of the following additions and subtractions in the 8-bit sign-and-magnitude binary number system.
    (i) 00101010 + 10101011     (ii) 10101010 + 10101010
    (iii) 11010101 − 01010101     (iv) 10101011 − 10101010

  (d) Show the result of the following multiplication of 8-bit two’s complement binary numbers in the 16-bit two’s complement binary representation.
    01110111 × 10001000

(2) Explain the procedure of addition of floating-point numbers

(3) Explain ‘data addressing modes’ in processors.

Kai​

(1)​

(a)​

  • (i) +88: 01011000
  • (ii) −72: . Two’s complement: invert 10110111, add 1 10111000

(b)​

  • (i) 10101010: Negative. Magnitude: invert 01010101, add 1 01010110 (86). Sign-and-magnitude 11010110
  • (ii) 11010101: Negative. Magnitude: invert 00101010, add 1 00101011 (43). Sign-and-magnitude 10101011

(c)​

  • (i) 00101010 + 10101011: 10000001
  • (ii) 10101010 + 10101010: 11010100
  • (iii) 11010101 − 01010101: . Since , it results in overflow.
  • (iv) 10101011 − 10101010: 10000001

(d)​

Multiply 01110111 (+119) and 10001000 (-120):

  • Product:
  • Magnitude:
  • Two’s complement for -14280: invert 1100100000110111, add 1 1100100000111000

Result: 1100100000111000

(2)​

  1. Unpack: Extract sign, exponent, and significand.
  2. Align: Shift significand of the smaller-exponent number until exponents match.
  3. Add/Subtract: Perform operation on significands based on signs.
  4. Normalize: Shift result to standard form and adjust exponent.
  5. Round: Round the significand to the available precision.
  6. Check: Verify exceptions (overflow, underflow, zero).

(3)​

Addressing modes define how instructions locate operands:

  • Immediate/Implied: Operand is constant within the instruction or implied by the opcode.
  • Register: Operand is stored in a CPU register.
  • Direct/Indirect: Address is directly in instruction, or instruction points to a pointer in memory.
  • Register Indirect: A register holds the memory address (pointer).
  • Indexed/Offset: Effective address = Base + Index or Base + Constant offset (common for arrays/stacks).
  • PC-relative: Address is an offset from the Program Counter (used for branches).
  • Auto-inc/dec: Register indirect with automatic address update before/after access.
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