Hw12#5
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This document provides instructions for homework assignment 12 due on December 21, 2015. It involves implementing high precision arithmetic functions for adding, subtracting, multiplying and scanning high precision numbers. As an example, it shows how to add and subtract the numbers 1.0947 and 0.00248 by aligning the decimal points and then performing the operations digit-by-digit, accounting for carries and borrows. Multiplication is shown by multiplying the digits of each number individually and adding them with carries into the answer array.
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The document discusses combinational logic circuits. It describes combinational logic design procedures including specification, formulation, optimization, technology mapping, and verification. It also discusses analysis procedures for logic diagrams, including labeling gate outputs and determining Boolean functions. Additional topics covered include half adders, full adders, binary adders, decoders, encoders, multiplexers, priority encoders, and binary-coded decimal to seven-segment displays. Diagrams and truth tables are provided for various logic gates and circuits.
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This document discusses arithmetic operations for computers including addition, subtraction, and overflow. It provides examples of adding and subtracting numbers in binary format. It explains the basic rules for addition and subtraction of binary numbers. It also discusses overflow that can occur during arithmetic operations and how overflow is handled differently for signed versus unsigned integers in MIPS computers. Overflow is detected using exceptions in MIPS.
LOGIC GATES - SARTHAK YADAV
This document provides an overview of logic gates and Boolean algebra. It discusses logic gates like AND, OR, and NOT. It reviews Boolean algebra concepts such as Boolean variables being limited to 1 or 0. It also covers converting between Boolean expressions and logic circuits, adding binary numbers, and memory elements like flip-flops.
Number system arithmetic
This document discusses different number systems including binary, octal, hexadecimal, and their arithmetic operations. It provides examples of adding and subtracting numbers in these systems. Binary addition follows four rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10. Octal addition is like decimal addition except when the column sum is greater than 7, 8 is subtracted and 1 is carried. Hexadecimal uses numbers 0-9 and letters A-F to represent values 10-15. It provides a table of decimal and hexadecimal equivalents. Hexadecimal addition involves treating multi-digit numbers as in decimal. Subtraction uses two's complement or 15's and 16's complement methods.
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Review on Number Systems: Decimal, Binary, and Hexadecimal
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Hw12#5
- 2. Problem 05. 可參考第一題的code生成high_precision.h和high_precision.c high_precision_t有三個屬性: digit(值), decpt(次方), sign(正負號) 0.0094328的表示 需實作add_high(), subtract_high(), multiply_high(), scan_high(), print_high()
- 3. 假設我們現在有1.0947和0.00248兩個數字 作加減運算的第一個步驟：小數點對齊→1-(-2)=3 1 0 9 4 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 0 0 2 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1
- 4. 相加 Sum = a + b + carry 1 0 9 4 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 9 7 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0
- 5. 相減 Diff = a - b - borrow 1 0 9 4 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 9 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
- 6. 相乘 1 0 9 4 7 2 4 8 2 7 1 4 8 5 6 1 0 9 4 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ans.digit[i+j+1] += a.digit[i] * b.digit[j] + carry; 1 7 3 6 9 9 2 2 2 3 2 0 2 4 8