Description

● Eight-bit Adder
One Bit Full Adder
A full adder is a combinational circuit that performs that adds two bits and a carry and outputs a sum bit and a carry bit. When we want to add two binary numbers, each having two or more bits, then we can use a one-bit adder as a submodule and give output as sum and carry out. The carry resulting from the addition of the LSBs is carried over to the next significant column and added to the two bits in that column. So, in the second and higher columns, the two data bits of that column and the carry bit generated from the addition in the previous column need to be added.
Truth Table of One Bit Full Adder
INPUT OUTPUT
A B Cin Sum Cout
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
K-map of One Bit Full Adder
K map of Sum output Bit
AB Cin
0 1
00 0 1
01 1 0
11 0 1
10 1 0
K map of Carry-Out output Bit 𝑆𝑢𝑚 = (𝐴 ⊕ 𝐵 ⊕ 𝐶𝑖𝑛)
AB Cin
0 1
00 0 0
01 0 1
11 1 1
10 0 1
𝐶𝑜𝑢𝑡 = ( 𝐴 . 𝐵 ) + 𝐶𝑖𝑛 . ( 𝐴 ⊕ 𝐵 )
Logic Circuit of One Bit Full Adder
8-Bit Full Adder Block Diagram

● Eight-Bit Full Subtractor
We will make Eight Bit Full Subtractor using One-bit Full Subtractor as a submodule.
One-Bit Full Subtractor
A full subtractor is a combinational circuit that subtracts two bits and borrow and outputs a difference bit and a borrow out bit. When we want to subtract two binary numbers, each having two or more bits, then we can use a one-bit subtractor as a submodule and give output as Difference and Borrow out. The borrow resulting from the addition of the LSBs is carried over to the next significant column and subtracted from the two bits in that column. So, in the second and higher columns, the two data bits of that column and the borrow bit generated from the subtraction in the previous column need to be subtracted.
Truth Table of One Bit Full Subtractor
INPUT OUTPUT
Borrow_in B A Difference Borrow_out
0 0 0 0 0
0 0 1 1 0
0 1 0 1 1
0 1 1 0 0
1 0 0 1 1
1 0 1 0 0
1 1 0 0 1
1 1 1 1 1
K-Map of One Bit Full Subtractor
K map of Difference output Bit
AB Bin
0 1
00 0 1
01 1 0
11 0 1
10 1 0
𝐷𝑖𝑓𝑓 = ( 𝐴 ⊕ 𝐵 ⊕ 𝐵𝑖𝑛 )
K map of Borrow-Out output Bit
AB Bin
0 1
00 0 1
01 1 1
11 0 1
10 0 0

𝐵𝑜𝑢𝑡 = ( 𝐴‾ . 𝐵 ) +𝐵𝑖𝑛 . ( 𝐴 ⊕ 𝐵 )
Logic Circuit of One Bit Full Subtractor

Block Diagram of One Bit Full Subtractor

8-Bit Full Subtractor Block Diagram

● Eight-Bit Adder Subtractor
On combining Logic of both Adder and Subtractor, we came to the conclusion that
For One-Bit Full Adder/Subtractor : 𝑆𝑢𝑚 / 𝐷𝑖𝑓𝑓 = ( 𝐴 ⊕ 𝐵 ⊕ 𝐶𝑖𝑛 / 𝐵𝑖𝑛 ) (depending on the opcodeif opcode == 0) )
𝐶𝑜𝑢𝑡 ((if opcode == 1) 𝐵𝑜𝑢𝑡 = ( 𝐴‾ . 𝐵 ) + 𝐵𝑖𝑛 . ( 𝐴 𝐵 )
Circuit Diagram for Eight-Bit Adder Subtractor