Tocci ch 6 digital arithmetic operations and circuits

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Digital Arithmetic Operations and
Circuits

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Binary Addition
Binary Addition

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Representing Signed Numbers

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Addition in 2’s Complement System

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Subtraction in 2’s Complement
System

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Multiplication of Binary
Numbers

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Binary Division

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BCD Addition

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Hexadecimal Arithmetic

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Arithmetic Circuits

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Arithmetic Circuits
ALU accepts data From memory, and executes
operations as instructed by the control unit.

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Add a number from the memory to the Accumulator
contents.
Arithmetic Circuits

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The number is transferred from memory to the B
register.
Arithmetic Circuits

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The numbers in B register and accumulator register are
added in the logic circuit, with sum sent to accumulator
for storage.
Arithmetic Circuits

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The new number remains in the accumulator for further
operations—or can be transferred to memory for storage
Arithmetic Circuits

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Parallel Binary Adder

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Parallel Binary Adder

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Design of a Full Adder

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Design of a Full Adder

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Complete Parallel Adder with Registers
Four-bit parallel adder circuit,
including the storage registers.

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Complete Parallel Adder with Registers

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Carry Propagation
• Limits parallel adder speed.
• called carry ripple.
• Look-ahead carry: to reduce the propagation
delay.

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Integrated Circuit Parallel Adder

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Integrated Circuit Parallel Adder

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2’s Complement System

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2’s Complement System

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2’s Complement System
• The adder/subtractor circuit has two control
signals ADD and SUB.
– ADD: A + B.
– SUB: A ─ B.

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Combined Addition and Subtraction
B0 𝐴𝑑𝑑/𝑆𝑢𝑏

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ALU Integrated Circuits
The 74LS382 (TTL) and
HC382 (CMOS) is a typical
device with 8 functions.

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Troubleshooting Case Study
• Determine the most likely fault…
Mode 1:
ADD = 0, SUB = 0.
Σ = A + 1.
Mode 2:
ADD = 1, SUB =
0.
Σ = A + B + 1.
Mode 3:
ADD = 0, SUB = 1.
Σ = [A] - [B].