Digital Logic · Unit 1 · 6 hrs
Binary Systems
Exam-focused notes for Binary Systems (Digital Logic, CSC116): what the TU syllabus asks and how it has actually been tested, with 7 solved past questions from this unit.
What this unit covers
- Digital Systems
- Binary numbers
- Number base conversion
- Octal and hexadecimal numbers
- compliments
- Signed Binary numbers
- Decimal codes (BCD, 2 4 2 1,8 4 -2 -1,Excess 3, Gray Code)
- Binary Storage and Registers
- Binary logic
compliments
Given A=46 and B=35 represent them in binary and perform A-B using 1's complement method. [5]
- $A = 46$ (minuend) - $B = 35$ (subtrahend) - Operation: $A - B$ using 1's complement. $46{10}$: $32+8+4+2 = 46 \Rightarrow 0010\,1110$ $35{10}$: $32+2+1 = 35 \Rightarrow 0010\,0011$ Decimal Binary (8-bit) ------------------------ $A = 46$ $0010\,1110$ $B ...
Full solved answer →Question
Perform the following operations:
a. $(0111010)_2 - (110011)_2$ using 2's complement
b. $(89344){10} - (98654){10}$ using 9's complement
[2.5+2.5]
- Part (a): $(0111010)2 - (110011)2$ using 2's complement - Part (b): $(89344){10} - (98654){10}$ using 9's complement --- - Minuend: $0111010$ (7 bits) - Subtrahend: $110011 \to 0110011$ (padded to 7 bits) 1's complement (flip bits): $$0110011 \to 1001100$...
Full solved answer →Carry out the following tasks:a. Perform 2's complement subtraction of 010110 - 100101b. Represent decimal number 10 in its BCD form [5]
- Part a: Subtraction $010110 - 100101$ (both 6-bit binary numbers) - Part b: Represent decimal 10 in BCD --- - Minuend $A = 010110$ - Subtrahend $B = 100101$ 1's complement (invert bits): $$100101 \rightarrow 011010$$ Add 1: $$011010 + 1 = 011011$$ So 2's ...
Full solved answer →Carry out the following tasks: a. Perform 1's complement subtraction of 10101-100101 b. Represent decimal number 0.125 into its binary form [2.5+2.5]
- Part (a): Subtraction $10101 - 100101$ using 1's complement method - Part (b): Convert decimal $0.125$ to binary --- - Minuend: $10101 = 21{10}$ - Subtrahend: $100101 = 37{10}$ Pad minuend to 6 bits: - Minuend: $010101$ - Subtrahend: $100101$ Flip all bit...
Full solved answer →Binary logic
Write short notes on (Any Two): Negative Logic, CMOS, EBCDIC [5]
--- Definition: In digital systems, logic levels are represented by two voltage levels. The assignment of these voltage levels to logic 0 and logic 1 defines the logic convention used. - In Positive Logic: The higher voltage level represents logic 1 and the...
Full solved answer →Signed Binary numbers
List two major characteristics of digital computer. Represent -6 (negative six) using 8 bits in signed magnitude, signed-1's-complement and signed-2's-complement respectively. Represent decimal number 4673 in a) octal, and b) BCD. [5]
- Number to represent in 8-bit signed forms: $-6$ - Decimal number to convert: $4673$ (to octal and BCD) --- 1. Operates on discrete/binary data: A digital computer represents and processes all data as discrete binary values (0s and 1s) using logic gates. 2...
Full solved answer →Number base conversion
Convert the following decimal numbers to the indicated bases. a) 7562.45 to octal b) 1938.257 to hexadecimal c) 175.175 to binary [2+1.5+1.5]
- a) $7562.45{10}$ to octal (base 8) - b) $1938.257{10}$ to hexadecimal (base 16) - c) $175.175{10}$ to binary (base 2) --- Division Quotient Remainder ------------------------------- $7562 \div 8$ 945 2 (LSB) $945 \div 8$ 118 1 $118 \div 8$ 14 6 $14 \div 8...
Full solved answer →Make Unit 1 stick
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