CS 1105-01 – AY2025-T4 Assignment Activity Unit 4 | Verified
study complete solutions | A+ Graded | 2026 Updated
CS 1105-01 - AY2025-T4
Assignment Activity Unit 4
Designing a Digital Calculator for Binary Arithmetic
Introduction
Binary arithmetic is fundamental to digital computation, forming the basis of all modern
computing systems. Designing a digital calculator that performs binary addition, subtraction,
multiplication, and division showcases the efficiency and versatility of binary computation. This
assignment explores the design and development of binary arithmetic modules, their
integration into a CPU, examples of binary calculations, advantages and challenges of binary
arithmetic, and the significance of such a calculator in understanding number systems.
1. Designing and Developing Binary Arithmetic Modules
To implement a digital calculator capable of performing binary arithmetic, four key modules—
binary adder, subtractor, multiplier, and divider—must be developed.
Binary Adder
A binary adder performs addition on two binary numbers. The most common implementation is
the full adder, which adds two bits along with a carry bit from the previous stage.
• Design Approach: o Use half adders to compute the sum of two bits. o Chain multiple
full adders to handle multi-bit binary numbers. o Implement a carry propagation
mechanism to ensure correct addition.
• Logic Table for a Full Adder: | A | B | Cin | Sum | Cout | |---|---|-----|-----|------| | 0 |
0|0|
, 0|0||0|1|0|1|0||1|0|0|1|0||1|1|0|0|1||0|0|1|1|0||0|
1|1|0|1||1|0|1|0|1||1|1|1|1|1|
Binary Subtractor
A binary subtractor computes the difference between two binary numbers using the two’s
complement method.
Design Approach:
o Convert the subtrahend into its two’s complement.
o Use a binary adder to add the two’s complement of the subtrahend to the
minuend. o Handle borrow propagation for multi-bit subtraction.
Binary Multiplier
Binary multiplication is performed using bitwise shifting and addition.
Design Approach: o Use the shift-and-add method, similar to decimal
multiplication. o Multiply each bit of the second operand by the first
operand. o Shift the partial products accordingly and sum them using a
binary adder.
Binary Divider
Binary division follows the long division method, similar to decimal division.
Design Approach: o Use successive subtraction to determine the
quotient. o Implement a restoring or non-restoring division
algorithm.
o Maintain a remainder register for accurate division results.
2. Integration and Organization of Modules
To ensure seamless mathematical operations, the binary arithmetic modules must be integrated
into a central processing unit (CPU) within the calculator.
Integration Strategy
• Arithmetic Logic Unit (ALU): The ALU will house the adder, subtractor, multiplier, and
divider modules.
study complete solutions | A+ Graded | 2026 Updated
CS 1105-01 - AY2025-T4
Assignment Activity Unit 4
Designing a Digital Calculator for Binary Arithmetic
Introduction
Binary arithmetic is fundamental to digital computation, forming the basis of all modern
computing systems. Designing a digital calculator that performs binary addition, subtraction,
multiplication, and division showcases the efficiency and versatility of binary computation. This
assignment explores the design and development of binary arithmetic modules, their
integration into a CPU, examples of binary calculations, advantages and challenges of binary
arithmetic, and the significance of such a calculator in understanding number systems.
1. Designing and Developing Binary Arithmetic Modules
To implement a digital calculator capable of performing binary arithmetic, four key modules—
binary adder, subtractor, multiplier, and divider—must be developed.
Binary Adder
A binary adder performs addition on two binary numbers. The most common implementation is
the full adder, which adds two bits along with a carry bit from the previous stage.
• Design Approach: o Use half adders to compute the sum of two bits. o Chain multiple
full adders to handle multi-bit binary numbers. o Implement a carry propagation
mechanism to ensure correct addition.
• Logic Table for a Full Adder: | A | B | Cin | Sum | Cout | |---|---|-----|-----|------| | 0 |
0|0|
, 0|0||0|1|0|1|0||1|0|0|1|0||1|1|0|0|1||0|0|1|1|0||0|
1|1|0|1||1|0|1|0|1||1|1|1|1|1|
Binary Subtractor
A binary subtractor computes the difference between two binary numbers using the two’s
complement method.
Design Approach:
o Convert the subtrahend into its two’s complement.
o Use a binary adder to add the two’s complement of the subtrahend to the
minuend. o Handle borrow propagation for multi-bit subtraction.
Binary Multiplier
Binary multiplication is performed using bitwise shifting and addition.
Design Approach: o Use the shift-and-add method, similar to decimal
multiplication. o Multiply each bit of the second operand by the first
operand. o Shift the partial products accordingly and sum them using a
binary adder.
Binary Divider
Binary division follows the long division method, similar to decimal division.
Design Approach: o Use successive subtraction to determine the
quotient. o Implement a restoring or non-restoring division
algorithm.
o Maintain a remainder register for accurate division results.
2. Integration and Organization of Modules
To ensure seamless mathematical operations, the binary arithmetic modules must be integrated
into a central processing unit (CPU) within the calculator.
Integration Strategy
• Arithmetic Logic Unit (ALU): The ALU will house the adder, subtractor, multiplier, and
divider modules.
