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Final Exam Exercise Problems
By Naufal Hartono
June 13, 2026
1. Number Systems and Binary Representation
a) Change the numbers:
i) 401 8 to 12-bit binary number system. Show the steps. ii) 53 10 to 12-bit binary number system. Show the steps.
b) What is the representation of the following numbers in:
i) 8-bit sign-and-magnitude ii) 8-bit two’s complement
a) +134 8 b) − (^8910)
c) 000110102 and 11101110 2 are two integers in one’s complement. Show the arithmetic operation to add these two integers.
d) Show the calculation for the operation 28 − 10 in 8-bit two’s complement represen- tation.
e) Change the numbers:
i) 157 8 ii) 101 10 iii) 3C (^616)
to 10-bit binary number system. Show the steps.
f ) What are the representations of:
i) +144 8 ii) − (^9810)
in:
a) 8-bit sign-and-magnitude b) 8-bit two’s complement
g) Show the calculation for − 2 − (−10) in one’s complement (8-bit).
h) Show the calculation for 18 − 13 in two’s complement (8-bit).
- Logic Circuits, Truth Tables, and Karnaugh Maps
a) Draw the logical circuit for the following logical expression:
F = A + BC + D
b) Draw the logical circuit for the following logical expression:
Q = (AB) + (A + B)
c) Draw the logic circuit for:
A
B
C
D
E
F
d) Draw a logic circuit for: G = AB + AC
e) Draw the circuit for (d) using ONLY NAND gates.
f ) Provide logical expression for the logical table below.
A B C X 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0
g) Create the truth table for: F = X(Y + Z) + Y Z
h) From the truth table, develop the Karnaugh map and provide the final F.
A B C F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1
iv) All entries except left-bottom corner
BC=00 BC=10 BC=11 BC=
A=
A=
v) All entries except middle bottom
BC=00 BC=10 BC=11 BC=
A=
A=
vi) Provide logical expression for the logical table below.
A B C D F 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0
- Assembly Language Analysis
a) What is the final value in register CH?
A DB 00110101B ; 0x B DB 00001111B ; 0x0F
MOV CX, 0000H
MOV CL, A
SUB CL, B
CMP CL, 10H
JNE L
MOV CH, B
L1: ADD CH, A
b) What is the final value in register AH?
P DB 10011001B ; 0x Q DB 00010001B ; 0x
MOV AX, 0000H
MOV AL, P
ADD AL, Q
CMP AL, 0A0H
JE L
MOV AH, Q
L2: SUB AH, P
c) What are the final values of AL and AH?
MOV AL, 05H
MOV AH, 02H
ADD AL, AH
MOV BL, 07H
DIV BL
d) What are the final values of AX and DX?
MOV AX, 0F00H
ADD AX, 0200H
MOV DX, 0000H
MOV CX, 0010H
DIV CX
